If (x-y)^2 = 100 and xy =20, what is the value of x^2 + y^2?

Question

1.) 120

2.) 140

3.) 80

4.) 60

Answer 1

Given (x-y)² = 100

x² - 2xy + y² = 100

x² + y² = 100 + 2xy = 100 + xy + xy

= 100 + 20 + 20

= 140.

Answer 2

First you will want to expand (x-y)²=100. This will yield x²-2xy+y²=100. We can now plug in xy=20.

This will give us x²-40+y²=100. Add over the 40 and x²+y²=140.

Hope this helps!