Question

If a² + b² = 41 and ab = 20, then (a + b) ÷ (a – b) = ______.
1. 9
2. 5
3. 7
4. 13

Answer 1

Correct Answer - Option 1 : 9

Concept:

(a + b)² = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculation:

Given:

a2 + b2 = 41 and ab = 20

(a + b)2 = 41 + (2 × 20) = 81

\((a + b) = \sqrt {81}\)

(a + b) = 9

(a - b)2 = 41 - (2 × 20) = 1

(a - b) = 1

\((a + b) ÷ (a – b) = \frac{(a+b)}{(a-b)}=\frac{9}{1}=9\)