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

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)
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  2. 4
  3. 3
  4. 6

Answer (Detailed Solution Below)

Option 3 : 3
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Detailed Solution

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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.

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