Question
Download Solution PDFIf a + b + c = 5, a3 + b3 + c3 = 85 and abc = 25, then find the value of a2 + b2+ c2 - ab - bc - ca.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
a + b + c = 5
a3 + b3 + c3 = 85
a × b × c = 25
Formula used:
a3 + b3 + c3 - 3 × a × b × c = (a + b + c)(a2 + b2+ c2 - ab - bc - ca)
Calculation:
⇒ (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
∴ The correct answer is 2.
Last updated on Jun 13, 2025
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