ఒకవేళ (a + b + c) = 20, మరియు aa2 + b2 + c2 = 152 అయితే, a3 + b3 + c- 3abc విలువను కనుగొనండి?

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SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 4)
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  1. 560
  2. 640
  3. 480
  4. 720

Answer (Detailed Solution Below)

Option 1 : 560
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ఉపయోగించిన  సూత్రం:

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

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

గణన :

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

⇒ 400 = 152 + 2(ab + bc + ca)

⇒ 248 = 2(ab + bc+ ca)

⇒ (ab + bc + ca) = 124

ఇప్పుడు,  a+ b+ c−3abc = (a + b + c) [a2 + b2 +c2 − (ab + bc + ca)]

⇒ 20 [152 - 124]

⇒ 28 × 20

⇒ 560

∴ సరైన సమాధానం 560.

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