SSC CGL 2023 PYQ — Question 71

The correct answer is option 1 i.e. 560.

Given that

If (a + b + c) = 20, a² + b² + c² = 152

Formula used

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

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

Calculation

⇒ 20² = 152 + 2(ab + bc + ca)

⇒ ab + bc + ca = (400 - 152)/2

⇒ ab + bc + ca = 248/2 = 124

Hence, a³ + b³ + c³ - 3abc = 20 × (152 - 124) = 20 × 28 = 560