A Cool Question

Algebra Level 2

I have two equations.

12 − x 2 − 2 x y = 0 12-x^{2}-2xy=0

12 − y 2 − 2 x y = 0 12-y^{2}-2xy=0

What is the largest solution for x+y?


The answer is 4.

Super Chicken by Super Chicken , 26, USA

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1 solution

From the two equations, we know that x^2 = y^2 and both x and y are positive or both negative.
so, x=y. Substitute y as x, give 12-x^2-2xx=0
Solving that equation, x=2 or x=-2
thus, x+y=4 or x+y=-4. My answer was 4


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