If \({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca} = -2\) and a + b = 5c, where c > 0, then the value of c is ________________.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 4)

Answer 1

Given :

\({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca} = -2\)

Formula used :

(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ca

Calculations :

According to the question

\({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca}\) = - 2

⇒ a2 + b2 + c² - 1024 = -2ab + 2bc + 2ca

⇒ a2 + b2 + c2 + 2ab - 2bc - 2ca = 1024

⇒ (a + b - c)² = 1024

⇒ a + b - c = 32

Put a + b = 5c

⇒ 5c - c = 32

⇒ 4c = 32

c = 8

∴ Option 1 is the correct choice.