Question
Download Solution PDFयदि a + b + c = 5, a3 + b3 + c3 = 85 और abc = 25 है, तो a2 + b2+ c2 - ab - bc - ca का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
a + b + c = 5
a3 + b3 + c3 = 85
a × b × c = 25
प्रयुक्त सूत्र:
a3 + b3 + c3 - 3 × a × b × c = (a + b + c)(a2 + b2+ c2 - ab - bc - ca)
गणना:
⇒ (a + b + c)(a2 + b2+ c2 - ab - bc - ca) = a3 + b3 + c3 - 3 × a × b × c
⇒ 5 × (a2 + b2+ c2 - ab - bc - ca) = 85 - (3 × 25)
⇒ (a2 + b2+ c2 - ab - bc - ca) = 10/5 = 2
∴ सही उत्तर 2 है।
Last updated on Jul 8, 2025
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