Question
Download Solution PDFयदि (a + b + c) = 12, और (a2 + b2 + c2) = 50 है, (a3 + b3 + c3 - 3abc) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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।
Last updated on Jul 8, 2025
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