Question

If x + y = 16 and xy = 18, find the value of 2(x - y)².
1. 368
2. 863
3. 638
4. 886

Answer 1

Correct Answer - Option 1 : 368

Concept:

(x - y)² = x² - 2xy + y²

(x + y)² = x2 + 2xy + y2

Calculation:

(x + y) = 16

Squaring both the sides

⇒ (x + y)² = (16)²

⇒ x² + 2xy + y² = 256

⇒ x2 + (2 × 18) + y2 = 256

⇒ x2 + y2 = 220

(x - y)2 = x2 - 2xy + y2

⇒ (x - y)2 = 220 - 2(18)

⇒ (x - y)2 = 220 - 36

⇒ (x - y)2 = 184

2(x - y)2 = 2 × 184 = 368

∴ 2(x - y)2 = 368

The correct option is 1 i.e. 368