If a = 101, b = 102 and c = 103, then a² + b² + c² − ab − bc − ca = _______.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)

Answer 1

Given

a = 101, b = 102 and c = 103

Formula used

1/2[(a - b)² + (b - c)² + (c - a)²] = a2 + b2 + c2 − ab − bc − ca

Calculation

⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[(a - b)2 + (b - c)2 + (c - a)2]

⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[(101 - 102)2 + (102 - 103)2 + (103 - 101)2]

⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[12 + 12 + 22]

⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[6]

⇒ a2 + b2 + c2 − ab − bc − ca = 3

The value is 3.