Question

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

Answer 1

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

$(x + y) ^2 = 105$

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

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


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

$65 + 2xy = 105$

$2xy = 105 - 65$

$2xy = 40$

$xy = 20$

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