What is the value of x^2+y^2?

Question

if x+y=10 and x−y=8
i got 52(x=6, y=4) but its wrong

Answer 1

let's add x+y=10 and x−y=8
2x = 18
x = 9
back in x+y=10, y = 1

now use those values.

(your solution of x=6, y=4
does not satisfy x+y=10 and x−y=8
your x+y = 10, but your x-y=2 , not 8)

Answer 2

(x+y)^2 + (x-y)^2
= x^2+2xy+y^2 + x^2-2xy+y^2
= 2(x^2+y^2)

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