SSC CPO 2020 PYQ — Question 112

The correct answer is Option 4 i.e. 2√10.

a² + b² + c² + 84 = 4(a - 2b + 4c)

Rearranging the equation

⇒ a² + b² + c² + 84 - 4a + 8b - 16c = 0

⇒ a² - 4a + 4 + b² + 8b + 16 + c² - 16c + 64 = 0

⇒ (a - 2)² + (b + 4)² + (c - 8)² = 0

If (a - b)² + (b - c)² + (c - a)² = 0

Then, (a - b) = 0

⇒ a = b, b = c, c = a

⇒ a = 2, b = -4, c = 8

Then,

⇒ $\sqrt{ab-bc+ca}$

⇒ $\sqrt{(2\times-4)-(8\times-4)+(8\times2)}$

⇒ $\sqrt{-8 - (-32) + 16}$

⇒ $\sqrt 40$ = $2\sqrt10$

Thus, $\sqrt{ab-bc+ca}$ = $2\sqrt10$