Question

If x ≠ y and (x + y)² = (x - y)², then which of the following must be true?
1. x + y = x - y
2. x + y = -(x - y)
3. x = 0
4. xy = 0

Answer 1

Correct Answer - Option 4 : xy = 0

Given:

If x ≠ y and (x + y)2 = (x - y)2

Formula used:

(a + b)² = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculation 

(x + y)2 = (x - y)²

⇒ x² + y² + 2xy = x² + y² - 2xy 

⇒ 4xy = 0 

⇒ xy = 0 

∴ The required answer is xy = 0