Given that x² + y² = 145 and x + y = 17, find the value of xy

Answer 1

To solve for the value of xy, we can use the identity (x + y)² = x² + 2xy + y².

We are given that x + y = 17.
Squaring both sides of the equation, we get:
(17)² = x² + 2xy + y²
289 = x² + 2xy + y² ....(1)

We are also given that x² + y² = 145.
Substituting this value into equation (1), we get:
289 = 145 + 2xy
289 - 145 = 2xy
144 = 2xy

Dividing both sides of the equation by 2, we find:
72 = xy

Therefore, the value of xy is 72.