If (a + b + c) = 13, and (ab + bc + ca) = 54, find the value of (a2 + b2 + c2).

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SSC CGL 2023 Tier-I Official Paper (Held On: 26 Jul 2023 Shift 2)
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  1. 63
  2. 65
  3. 61
  4. 59

Answer (Detailed Solution Below)

Option 3 : 61
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Detailed Solution

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Formula used:

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

Calculation:

⇒ 132a2 + b2 c2+ 2 × 54

⇒ 169 - 108 a2 + b2 c2

⇒ a2 + b2 + c2 = 61

∴ The correct option is 3

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