Math POTW for Secondary and High School Students Forum

MHB Prove: No Real Roots for Polynomial x^4-px^3+qx^2-sqrt(q)x+1
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MHB Are There Two Integer Solutions to This Quadratic Equation?
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MHB Proving Triangle Inequality for Sides and Opposite Angles in a Triangle
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MHB Can Integer Equations Reveal Perfect Square Patterns?
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MHB How Do Disjoint Intervals Solve the Inequality in POTW #409?
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MHB Minimum Value of $(u-v)^2$ and $\left(\sqrt{2-u^2}-\dfrac{9}{v}\right)^2$
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MHB Perfect Squares as Divisors of $1!\cdot 2! \cdot 3! \cdots 9!$
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MHB What Is the Smallest n Such That Sequence Sum S_n Exceeds 10000?
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MHB Reflection of Parabolas: Find the Sum of Coefficients - POTW #406 Feb 27th, 2020
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MHB Find the Smallest Divisible Integer: POTW #405 Feb 20th, 2020
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MHB What is the Largest Possible Value of BD in a Cyclic Quadrilateral?
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MHB Find the Minimum Values of Monic Quadratic Polynomials - POTW #403 Feb 2nd, 2020
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MHB Is ln(2) Greater Than (2/5)^(2/5)?
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MHB How Do You Calculate the Total Length of Intervals for x in This Inequality?
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MHB What is the Smallest Possible Value of a in This Polynomial Pattern?
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MHB How Do Triangle Sides Relate to Acute Angles?
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MHB Can You Solve This Sum of Floor Functions Challenge?
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MHB What Is the Sum of the Digits of 3n Given These Conditions?
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MHB Polynomial $P(x)$ Satisfying $P(k)=2^k$: POTW #396 Dec 9th, 2019
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MHB What is the solution for d in a trigonometric equation with multiple terms?
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MHB How Can We Prove the Inequality for Polynomial Roots in POTW #394?
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MHB Can You Solve This Trigonometric Inequality?
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MHB How to Calculate \(a+b+c\) for Equations Sharing Common Real Roots?
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MHB Can you solve this inequality involving positive real numbers?
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MHB How to solve for x in a nested polynomial equation?
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MHB How Many Real Roots Does This Equation Have?
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MHB How Can You Factorize the Polynomial (x+1)(x+2)(x+3)(x+6)-3x^2?
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MHB Can You Solve This Advanced Algebra Puzzle?
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MHB POTW #386: Evaluate (a+b+c)(b+c+d)(c+d+a)(d+a+b) for x^4-7x^3+3x^2-21x+1=0
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MHB Can You Solve the Exponential Equation for Integer Triples $(a, b, c)$?
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MHB How Do You Solve the Equation \(x^3(x+1) = 2(x+a)(x+2a)\) for Real \(a\)?
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MHB What is $a_{1996}$ in this series?
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MHB Inscribed Quadrilateral Perpendicular Bisectors Convergence Theorem
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MHB What Are the Non-Negative Integer Solutions to (xy-7)² = x² + y²?
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MHB Is There a Rational Multiple for the Product of Sines from 1 to 90 Degrees?
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MHB Alternate solution from MegaMoh:
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MHB Prove $a+b>c+d$ for Real Numbers with Sine Inequalities
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MHB How Do You Factor \(x^8+4x^2+4\) into Non-Constant Polynomials?
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MHB Can Polynomial Constraints Determine a Unique Integer Solution?
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MHB Can You Evaluate abc in This System of Cubic Equations?
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MHB POTW #374: Finding the 1000th Digit of the Square Root of a Large Number
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MHB Is ab+cd Not Prime in This Integer Puzzle?
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MHB POTW #372: Solve $4x^6-6x^2+2\sqrt{2}=0$ without a calculator - June 25th, 2019
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MHB How Long is Side CD in a Special Trapezium?
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MHB Can You Solve This Cubic and Square Root Equation?
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MHB Can Real Roots in a Quadratic Guarantee a Root in a Quartic?
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MHB Can You Prove $ab\le 1$ Given $(x+a)(x+b)=9$?
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MHB Can You Simplify This Complex Square Root Expression?
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MHB Maximizing $abcd$ with given constraints - POTW #366 May 14th, 2019
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MHB Proof of Convergence: Nested Radicals with Constant Sum on May 8, 2019
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MHB Prove: Sum of Cubed Roots of Trigonometric Expressions Equals Square Root of 9/2
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MHB How Do You Calculate the Sum of Minimum Values in Polynomials?
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MHB Can You Solve This Real Number System of Equations?
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MHB Prove Inequality: (a+2)(b+2) ≥ cd with a^2 + b^2 + c^2 + d^2 = 4
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MHB What is the value of $xy+yz+zx$ in a system of equations with real numbers?
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MHB Prove $a^2+b^2\ge 8$ for real roots of $x^4+ax^3+2x^2+bx+1=0$
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MHB Find the Minimum Non-Zero Value of A^2+B^2+C^2 with Integer Constraints
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MHB How Do Floor Functions Affect the Results of Square Roots in Sequence Problems?
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MHB Can Trigonometric Identities Simplify This Week's Complex Integral?
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MHB Prove the Sum of Cube Roots of Roots of a Cubic Equation is Zero
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MHB POTW #354: Find Possible Value of a-b When $x^2-x-1$ Divides $ax^{17}+bx^{16}+1$
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MHB How do I solve for non-negative integers x and y?
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MHB Can You Solve This High School Math Series Without a Calculator?
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MHB What is the integral of (x^2+1)/(e^x+1) from -1 to 1?
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MHB What is the Value of Angle MBC in the Triangle-Square Configuration?
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MHB Is the Number 2 Truly Persistent?
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MHB Is T Always Equal to 2 in the Persistent Number Theorem?
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MHB Can AC Be Less Than Twice FG in a Square Geometry Setup?
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MHB Solve Equation for Trigonometric Functions with Integer and Fractional Parts
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MHB Problem Of The Week #345 Dec 18th, 2018
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MHB Can You Solve for a, b, and c Given This Challenging Equation?
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MHB Can You Prove $\cos(\cos 1) > \sin(\sin(\sin 1))$?
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MHB Can You Crack This Week's Rational Equation Challenge?
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MHB How Do You Calculate the Sum of Cubed Tangents for Angles from 0 to 89 Degrees?
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MHB Solution for Roots of x^3-7x+7=0: Week #340 Nov 13th, 2018 POTW
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MHB Can You Solve This Challenging System of Real Number Equations?
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MHB How to Solve a Logarithmic Equation?
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MHB How to Prove Sin Equations with Given Constraints?
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MHB Can You Solve This Triangle Cotangent Ratio Problem?
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MHB How Do You Solve for \(x^4 + y^4\) Given These Equations?
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MHB How Does Cyclic Product Change for Polynomial Roots?
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MHB Real Numbers and Proportional Relationships: Solving for x, y, and z | POTW #333
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MHB When Is \( n^4 + 4 \) a Prime Number?
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MHB The Problem of the Week #331: How do you integrate the arcsine squared function?
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MHB Prove the Identity: sin(2x) + sin(2y) + sin(2z) = 4sin(x)sin(y)sin(z)
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MHB Can Ceva's Theorem Solve the Triangle Concurrency in POTW #329?
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MHB Minimum Natural Number for Fraction Expression #328 Aug 24, 2018 POTW
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MHB How Can You Prove That 83 Divides x in This Mathematical Series?
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MHB Find the Number of Polynomials with Coefficients in {0-9} That Satisfy P(-1)=-9
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MHB Can You Prove e^x Is Greater Than x^2 for All Positive x?
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MHB What Is the Missing Digit in \(1995^{10}\)?
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MHB How Do You Solve This Complex Integral Problem?
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MHB Probability of Satisfying Floor Inequality with Random Real Numbers
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MHB How to Solve for Unknown Variables with Given Equations?
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MHB How Can You Prove a Quadratic with No Real Roots Satisfies the Inequality?
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MHB What Is the Missing Digit in $2^{29}$?
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MHB Probability of Hitting Center of a Square Target - POTW #318 (Jun 13, 2018)
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MHB Can You Discover the Integer Pair That Satisfies This Unique Sum Equation?
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MHB Can This Complex Integral Be Proven Rational?
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MHB Are There Limited Ordered Triples for Complex Number Equations?
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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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