Question

If a² + b² = 2b + 4a – 5, then what is the value of 2(a + b)?
1. 10
2. 12
3. 8
4. 6

Answer 1

Correct Answer - Option 4 : 6

Given:

a2 + b2 = 2b + 4a – 5

Concept used:

If (x – a)² + (y –  b)² = 0

Then x – a = 0, y – b = 0

Formula used:

(x – y)² = x² + y² – 2xy

Calculations:

a2 + b2 = 2b + 4a – 5

⇒ a² – 4a + b² – 2b + 5 = 0

⇒ a² – 4a + 4 + b² – 2b + 1 = 0

⇒ (a – 2)² + (b – 1)² = 0

⇒ a – 2 = 0 and b – 1 = 0

⇒ a = 2 and b = 1

Thus 2(a + b) = 2(2 + 1) = 2 × 3 = 6

∴ The value of 2(a + b) = 6.