MHB Prove √(a^2+b^2)≤ √[(x−a)^2+(y−b)^2]+√(x^2+y^2)

  • Thread starter Thread starter solakis1
  • Start date Start date
AI Thread Summary
The discussion centers on proving the inequality √(a² + b²) ≤ √[(x - a)² + (y - b)²] + √(x² + y²). Participants express a desire for an algebraic solution rather than a graphical representation. The need for clarity in the proof is emphasized, with some participants reiterating the request for algebraic methods. The conversation highlights the importance of understanding the geometric implications of the inequality. Ultimately, the focus remains on finding a rigorous algebraic proof for the stated inequality.
solakis1
Messages
407
Reaction score
0
prove:

$$\sqrt{a^2+b^2}\leq\sqrt{(x-a)^2+(y-b)^2}+\sqrt{x^2+y^2}$$
 
Mathematics news on Phys.org
solakis said:
prove:

$$\sqrt{a^2+b^2}\leq\sqrt{(x-a)^2+(y-b)^2}+\sqrt{x^2+y^2}$$

This comes from law of triangle sides

distance from origin to (a,b) < distance from (x,y) to (a,b) + distance from origin to (x,y) and equal if (x,y) is between (0,0) and (a,b) and in the line between the 2
 
kaliprasad said:
This comes from law of triangle sides

distance from origin to (a,b) < distance from (x,y) to (a,b) + distance from origin to (x,y) and equal if (x,y) is between (0,0) and (a,b) and in the line between the 2

Can you draw a picture ??

I was meaning an algebraic solution in my OP
 
solakis said:
Can you draw a picture ??

I was meaning an algebraic solution in my OP

we have $\sqrt{(x-a)^2+(y-b)^2} + \sqrt{x^2+y^2} = |(x-a) + i(y-b)| + | x + iy| = | (a-x) + (b-y) i | + | x + iy|$
$\ge |(a - x + x) + i(b-y+y)| = | a + ib| = \sqrt{a^2+b^2}$
 
Last edited:

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
Replies
4
Views
1K
MHB Solving System of Equalities: x^2-y\sqrt xy & y^2-x\sqrt xy =3
Replies
2
Views
1K
MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
Replies
1
Views
2K
MHB Inequality c≤√[(x−a^2+(y−b)^2+(z−c)^2]+√(x2+y2+z2)
Replies
5
Views
1K
MHB Solve System of Equalities: x^2+xy+y^2, x^2+xz+z^2, y^2+yz+z^2
Replies
7
Views
1K
MHB What is the graph of y = sin^2 x + cos^2 x?
Replies
1
Views
1K
B What went wrong with (-x)^2=x^2?
Replies
22
Views
2K
MHB [ASK] Make x and y the Subjects: x^3-3xy^2=a, 3x^2y-y^3=b
Replies
6
Views
2K
MHB Can you solve for y in sin(y) - y = x√(2)?
Replies
4
Views
2K
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top