यदि (a + b + c) = 12, और (a2 + b2 + c2) = 50 है, (a3 + b3 + c3 - 3abc) का मान ज्ञात कीजिए।

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SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 2)
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  1. 36
  2. 24
  3. 42
  4. 48

Answer (Detailed Solution Below)

Option 1 : 36
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Detailed Solution

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दिया गया है: 

(a + b + c) = 12, (a2 + b2 + c2) = 50

प्रयुक्त सूत्र: 

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

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

गणना: 

⇒ 144 = 50 + 2(ab + bc +ac)

⇒ (ab + bc +ac) = 94/2 = 47

अब,

⇒ (a3 + b3 + c3 - 3abc) = (50 - 47)(12)

⇒ (a2 + b2 + c2 - ab - bc - ca)(a + b + c) = (50 - 47)(12)

⇒ 3 × 12 = 36

∴ सही उत्तर 36 है।

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