If x - y = 1 and x² + y² = 41, then the value of x + y will be?

Question: If x - y = 1 and x² + y² = 41, then the value of x + y will be?

Solution:
here, x - y = 1
⇒ (x - y)² = 1²
⇒ x² + y² - 2xy = 1
⇒ 41 - 2xy = 1 [as given, x² + y² = 41]
⇒ 2xy = 40

Now,
∴ (x + y)² = x² + y² + 2xy
⇒ (x + y)² = 41 + 40
⇒ (x + y)² = 81
⇒ (x + y) = 9