Question

If 2a + 3b = 8 and ab = 5, then find the value of 4a² + 9b².
1. 6
2. 8
3. 2
4. 4

Answer 1

Correct Answer - Option 4 : 4

Given:

2a + 3b = 8 

ab = 5

Formula used:

(x + y)² = x² + y² + 2xy

Calculations:

Squaring the given equation,

⇒ (2a + 3b)² = 64

⇒ 4a² + 9b² + 12ab = 64

Substituting the value of ab,

⇒ 4a² + 9b² + (12 ×  5) = 64

⇒ 4a2 + 9b2 = 64 – 60 = 4

∴ The value of 4a2 + 9b2 is 4