Question

If a² + b² = 25, x² + y² = 17 and ax + by = 8, then what is the value of (ay - bx)?
1. 25
2. 33
3. 19
4. 21

Answer 1

Correct Answer - Option 3 : 19

Given:

a2 + b2 = 25, x2 + y2 = 17, ax + by = 8 

Formulas used:

(a + b)² = a² + b² + 2ab

(a - b)² = a2 + b2 - 2ab

(ax + by)² + (ay - bx)² = (a2 + b2) × ( x2 + y2)

Calculation:

By using the above formula; 

(ax + by)2 + (ay - bx)2 = (a2 + b2) × ( x2 + y2)

⇒ 8² + (ay - bx)2 = 25 × 17

⇒  (ay - bx)2 = 425 - 64 = 361

⇒ (ay - bx) = √361 = 19 

∴  (ay - bx) = 19