If x - y = 3 and x² + y² = 45, then the value of x + y will be?

Question: If x - y = 3 and x² + y² = 45, then the value of x + y will be?

Solution:
We are given:
x - y = 3
⇒ x² + y² = 45

(x - y)² = x² + y² - 2xy
⇒ 3² = 45 - 2xy [Substitute x - y = 3]
⇒ 9 = 45 - 2xy
⇒ 2xy = 45 - 9
⇒ 2xy = 36
⇒ xy = 18

Again,
(x + y)² = x² + y² + 2xy
⇒ (x + y)² = 45 + 36 [Substitute the values]
⇒ (x + y)² = 81
⇒ x + y = 9