max+min of x + y ? x+y?

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For x x and y y that satisfy the inequality x 2 + y 2 6 x 10 y 26 , x^2 + y^2 - 6 x - 10 y \leq -26, what is the sum of the maximum and minimum values of x + y ? x + y ?

12 12 18 18 16 16 14 14

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1 solution

Kundan Chaudhary
Feb 22, 2014

differentiate the equation with respect to x, we get 2x + 2yy'-6-10y'<=0 we get x=3 and y=5+2(2^1/2),5-2(2^1/2) so max(x+y)=8+2(2^1/2) min(x+y)=8-2(2^1/2) so, sum of max and min of x+y=16.

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