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

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

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)

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

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

...

To find the value of x^2+y^2, you need to square both x and y individually and then sum them up.

Given the equations x+y=10 and x−y=8, you can solve this system of equations to determine the values of x and y.

First, let's solve for x by adding the two equations together:
(x+y) + (x-y) = 10 + 8
2x = 18
Dividing both sides by 2, you get:
x = 9

Next, substitute the value of x back into one of the original equations to solve for y. Let's use the equation x+y=10:
9+y = 10
Subtracting 9 from both sides, you get:
y = 1

Now that you have the values of x=9 and y=1, you can calculate x^2+y^2:
x^2 = 9^2 = 81
y^2 = 1^2 = 1

x^2 + y^2 = 81 + 1 = 82

So, the value of x^2+y^2 is 82, not 52.