Math POTW for Secondary and High School Students Forum

POTW Inequality of Positive Real Numbers: Proving (1-1/x^2)(1-1/y^2)≥9 with x+y≤1
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12
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1K
POTW Integer n: Solving the Equation ##\dfrac{n^2+3}{2n+4}## for Integers
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14
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1K
POTW Solve 3-Variable Equation with Real Solutions | √(z-y^2-6x-26)+x^2+6y+z-8=0
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3
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874
MHB Optimize Square Root Expression for Positive x and y - POTW #492 12/24/2021
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6
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1K
POTW Prove that the roots of a polynomial cannot be all real
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5
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986
MHB Proof of x(x+y) ≤ 2 for Positive Real Numbers | POTW #503 - June 24, 2022
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11
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1K
POTW Proving Inequality between Positive Real Numbers a and b: a(a+b) ≤ 2
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6
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916
MHB Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
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2
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937
POTW Find Triplets of Positive Integers with Sum of Cubes
2
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66
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3K
MHB POTW #499: Proving Trigonometric Identity with $\csc$ Functions
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1
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910
MHB Triangle ABC: Minimum value of (a^2+b^2)/c^2 | POTW #502 June 10th 2022
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1
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855
POTW Find the Sum of Two Real Numbers | Solve a + b with Given Equations
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19
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1K
MHB Is the product of two radical expressions equal to six?
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13
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1K
POTW Finding the Product of Real Roots: POTW Equation Solution
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9
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1K
MHB Maximize x: 2x+y+4/xy=10 (POTW #497 3/4/2022)
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7
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1K
MHB Find the Smallest Cosine Value | POTW #496 | February 15, 2022
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2
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889
MHB POTW #473: Solving for Pairs of Positive Integers (k,n) in a Factorial Equation
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4
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1K
MHB What is the minimum value of a+b+c+d if a^2-b^2+cd^2=2022?
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5
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970
MHB Minimum Value of (a+7)^2+(b+2)^2 with Constraint (a-5)^2+(b-7)^2=4 - POTW #506
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5
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894
MHB Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
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1
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786
MHB Real Solutions for Sin^5 x + Cos^3 x = 1 | POTW #500 - April 29th 2022
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1
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1K
MHB Solution to POTW #498: Is (1+1/2)(1+1/4)(1+1/6)...(1+1/2018) >, <, or = 50?
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1
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754
MHB Proof of Right-Angled Triangle from Problem #494 - Jan. 19, 2022 POTW
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1
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847
MHB Can You Solve POTW #493: Polynomial with Distinct Roots in Set M?
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1
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651
MHB Prove $2^{\sqrt{12}}>11 | POTW #491 Dec 14, 2021
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2
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909
MHB What is the Range of $w(w+x)(w+y)(w+z)$ When $x+y+z+w=x^7+y^7+z^7+w^7=0$?
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1
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813
MHB POTW #484: Integer Solutions of Quadratic Equations with Perfect Squares
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1
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799
MHB How many positive integral solutions $(x,\,y)$ are there for the equation $\dfrac{1}{x+1}+\dfrac{1}{y}+\dfrac{1}{y(x+1)}=\dfrac{1}{2015}$?
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1
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742
MHB What is the greatest 5-digit palindrome for 7n to be a 6-digit palindrome?
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1
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765
MHB How do you solve a system of equations with rational functions?
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1
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932
MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
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1
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780
MHB POTW #486: Evaluating Trigonometric Expressions for October 11th, 2021
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1
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711
MHB Prove $P(x)=0 \implies Q(x^2)=0 | POTW #485 Oct 4, 2021
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1
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725
MHB Can you solve this week's POTW about positive real numbers?
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1
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814
MHB Solution to POTW #481: Evaluating g(r1)g(r2)g(r3)g(r4)g(r5)
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1
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748
MHB Sum of Cosine Values for $x$ | POTW #480 8/24/2021 | $100^{\circ}<x<200^{\circ}$
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1
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894
MHB What is the value of (x+y)(y+z)(z+x) if 1/(x+y+z) = 1/x + 1/y + 1/z?
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1
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764
MHB Find All Positive Integer Pairs for (x, y) in sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1
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1
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830
MHB What's the solution to POTW #476?
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1
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780
MHB What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
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1
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739
MHB POTW #475: Evaluating a Tricky Fraction with a Mysterious Relationship
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1
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777
MHB Can you solve this week's POTW #474: Four real numbers with unique permutations?
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1
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788
MHB Largest Natural Number Divisibility Problem #472 - June 16th, 2021 POTW
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1
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888
MHB Discover the Area of Points in a Unit Square | POTW #471
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1
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751
MHB Solution to |x|+|y|+|z|=2010 - POTW #470 May 30th 2021
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2
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741
MHB Prove Inequality: Integral of Square Root vs. Trigonometric Function
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1
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735
MHB Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
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1
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748
MHB POTW #467: Solve for Positive Integers in (n^2+11n-4)*n!+33*13^n+4
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2
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766
MHB What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
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1
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837
MHB Finding Extremes of x^3+y^3+z^3+xyz for Real Numbers with Constraints
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1
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720
MHB System of Equations: Week #464 POTW (4/19/2021)
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1
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788
MHB Prime Numbers and Fifth Powers: POTW #462 (April 5th, 2021)
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1
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1K
MHB Can you solve this week's POTW: (x+1)(x+2)(x+5)≥36x?
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1
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845
MHB Triangle with Vertices A(0,0), B(3,4), C(2,c) | POTW #461 March 29 2021
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1
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710
MHB POTW #460: Proving Integer Coefficients of a Quadratic Function
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1
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815
MHB Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
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1
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835
MHB Is it possible to find 6-digit numbers with a sum of 8?
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1
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848
MHB Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
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1
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759
MHB POTW #456: Find the Value of (x+20)(y+20)(z+20) Given Three Equations
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1
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775
MHB Integer Solutions for System xz-2yt=3 and xt+yz=1 | POTW #455
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1
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886
MHB What is the Greatest Value of an Expression with Given Numbers and Equation?
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1
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839
MHB Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
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1
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887
MHB Can You Solve This Integer Equation for January 25th, 2021?
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3
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900
MHB Divisor Problem: $30^{2003}$ vs. $20^{2000}$ | POTW #451 Jan 18th 2021
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1
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792
MHB What are the solutions to x^3+3367=2^n?
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1
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1K
MHB Triangle ABC: Find Possible Values of Cos A | POTW #449 Jan 4th 2021
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2
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800
MHB How to solve the inequality in this week's POTW?
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2
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822
MHB POTW #447: Find Positive Values for a and b to Satisfy a Specific Equation
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1
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739
MHB Triangle with Complex Number Vertices SATISFIES Equilateral Relation
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1
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807
MHB Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
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1
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847
MHB Maximum Value of Square Root Expression with Three Variables in [0,1]
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2
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1K
MHB Triangle Perimeter Problem: POTW #443 - November 16th, 2020
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1
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799
MHB Prove: sin(x) ≥ 2x/π for 0 ≤ x ≤ π/2 | POTW #442 Nov. 9, 2020
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1
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824
MHB Convex Quadrilateral Problem - POTW #440 October 26th, 2020
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2
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941
MHB Prove |k| ≤ 1 for Cubic Equation with Real Numbers - POTW #441
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1
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792
MHB POTW #439: Proving Integer Property with Rational Numbers
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1
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766
MHB Prove: 0 < a < 1 < b < 3 < c < 4 | POTW #436 (Sept. 28, 2020)
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2
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822
MHB What are the solutions to a set of equations involving triple real numbers and specific conditions?
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1
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826
MHB Can You Solve a Cubic Equation with Real Coefficients? - POTW #437
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1
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896
MHB Find the Value of b | POTW #435 | September 21, 2020
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2
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838
MHB Quadratic Polynomial Problem: Proving Equality with Real Numbers
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1
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876
MHB Solution to Problem #433: Proving a+b+c=0 yields 9
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1
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832
MHB What is the Solution to POTW #432: Lattice Point Movement?
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1
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815
MHB What is the divisor formula for positive integers in POTW #431?
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1
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892
MHB Integers with Integer Roots | POTW #430 (Aug 18, 2020)
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1
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826
MHB Regular 12-Gon Inscribed in Circle: POTW #429 (August 10, 2020)
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1
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796
MHB Non-Calculus Solution for Divisible Polynomial | POTW #428 Aug 3, 2020
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2
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900
MHB Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
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1
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954
MHB The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
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1
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896
MHB POTW #425: Solving an Equation with Three Radicals
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1
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837
MHB Maximizing a in $ax^3+bx^2+cx+d$ with Constraints | POTW #424 07/06/2020
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1
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921
MHB Find $x^2+y^2+z^2+w^2$ using a system of equations | POTW #423 6/29/2020
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1
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861
MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
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1
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931
MHB What is the identity equation for solving natural numbers in POTW #421?
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1
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938
MHB Find the Sum of Real Numbers Satisfying Equations
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1
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937
MHB POTW #419: Probability of No One on a Bridge at Noon
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1
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930
MHB Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
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1
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923
MHB Acute Triangle ABC: Point P and Line Intersections Formula
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1
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807
MHB Positive Real Solutions to System of Equations - POTW #413 (Apr 19th, 2020)
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1
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1K
MHB Discover Non-Real Roots and Sum of Equation #416 - May 11th, 2020 POTW
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1
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1K
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POTW High School

Welcome to the High School POTW forum!

Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one math problem each week at the advanced high school student or secondary level.

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