Question

If (x + y)² - (x - y)² = 144, and (x + y) = 13, then what is the value of (x² + y²)?
1. 67
2. 77
3. 87
4. 97

Answer 1

Correct Answer - Option 4 : 97

Given:

(x + y)2 - (x - y)2 = 144

Concpet:

(a + b)² - (a - b)² = 4ab

(a + b)² = a² + b² + 2ab

Calculation:

⇒ (x + y)2 - (x - y)2 = 4 × 36

⇒ xy = 36

⇒ (x + y)² = x² + y² + 2xy

⇒ (13)² = x² + y² + 2 × (36)

⇒ x² + y² = 169 - 72

⇒ x² + y² = 97

∴ The required result will be 97.