Question

If (2a - 3)² + (3b - 5)² + (4c - 7)² = 0, then find the value of √(4a + 3b + 4c).

A. 6√2

B. 9√2

C. 12√2

D. 3√2

1. C
2. A
3. B
4. D

Answer 1

Correct Answer - Option 4 : D

Given:

(2a - 3)2 + (3b - 5)2 + (4c - 7)2 = 0

Formula Used:

If  (a - b)² + (b - c)² + (c -a)² = 0 then

a = b, b = c, c = a

Calculation:

(2a - 3)2 + (3b - 5)2 + (4c - 7)2 = 0

by using the Formula 

2a - 3 = 0

⇒ a = 3/2      ----(i)

3b - 5 = 0

⇒ b = 5/3      ----(ii)

4c - 7 = 0

⇒ c = 7/4      ----(iii)

Substituting the (i) (ii) (iii) in the √(4a + 3b + 4c).

√(4a + 3b + 4c) = √(4 × 3/2 + 3 × 5/3 + 4 × 7/4 ).

√(4a + 3b + 4c) = √(6 + 5 + 7) =√18 ⇒ 3√2

 ∴ The value of √(4a + 3b + 4c) is 3√2