Question

If a(a + b + c)² = 1792; b(a + b + c)² = 1536; c(a + b + c)² = 768 then what will be the value of a?
1. 9
2. 16
3. 7
4. 6

Answer 1

Correct Answer - Option 3 : 7

Given:

a(a + b + c)2 = 1792

b(a + b + c)2 = 1536

c(a + b + c)2 = 768

Calculation:

a(a + b + c)2 = 1792      ----(1)

b(a + b + c)2 = 1536      ----(2)

c(a + b + c)2 = 768      ----(3)

Add equation (1), (2) and (3)

⇒ a(a + b + c)2 + b(a + b + c)² + c(a + b + c)² = 1792 + 1536 + 768

⇒ (a + b + c)2 (a + b + c) = 4096

⇒ (a + b + c)³ = 4096

⇒ (a + b + c) = 16

From equation (1)

⇒ a × (16)² = 1792

⇒ a = 7

∴ The value of a is 7.