If x - y = 2 and x² + y² = 20, then find the value of x + y.

Question: If x - y = 2 and x² + y² = 20, then find the value of x + y.

Solution:
Given:
x - y = 2
x² + y² = 20
We know,
(x - y)² = x² + y² - 2xy

Substitute the given values:
2² = 20 - 2xy
4 = 20 - 2xy
2xy = 20 - 4
2xy = 16
⇒ xy = 8

Again,
(x + y)² = x² + y² + 2xy
(x + y)² = 20 + 16
(x + y)² = 36
⇒ x + y = √36
∴ x + y = 6