perplexus.info :: Just Math : Simultaneous inequality?

Simultaneous inequality? (Posted on 2023-07-15)

Solve following system equations:

3x+4y=26
√(x²+y²-4x+2y+5)+√(x²+y²-20x-10y+125)=10

No Solution Yet Submitted by Danish Ahmed Khan

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re: Solution

Comment 4 of 4 |

(In reply to Solution by Brian Smith)

My solution was very similar, I just thought of things a bit differently.

Simplify the second equation as you did but then see that

√(x²+y²-4x+2y+5)=a and

sqrt[(x-10)^2 + (y-5)^2]=b

Where a+b=10 would be two circles (a>0, b>0 of course)

one at (2,-1) with radius a and the other at (10,5).

These centers are also 10 apart, so they always have a common tangent on the line segment connecting their centers.

The rest is the same.

Posted by Jer on 2023-07-16 15:23:35

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