Question

If (x + y)^2 = 105 and x^2 + y^2 = 65, what is the value of xy?

Answer 1

`\boxed { \boxed {(a + b)^2 = a^2 + 2ab + b^2}}`


`(x + y) ^2 = 105`


`x^2 + 2xy + y^2 = 105`


`x^2 + y^2 + 2xy = 105`



`\text{Given that } x^2 + y^2 = 65,`


`65 + 2xy = 105`


`2xy = 105 - 65`


`2xy = 40`


`xy = 20`


`\boxed { \boxed {\text{Answer: xy = 20}}}`