Question
Download Solution PDFIf a + b + c = 6 and a2 + b2 + c2 = 40, then what is the value of a3 + b3 + c3 - 3abc?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
a + b + c = 6
a² + b² + c² = 40
Formula used:
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
Solution:
a + b + c = 6
⇒ (a + b + c)2 = 62
⇒ a2 + b2 + c2 + 2ab + 2bc + 2ac = 36
⇒ 40 + 2(ab + bc + ca) = 36
⇒ 2(ab + bc + ca) = - 4
⇒ ab + bc + ca = - 2
and
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
⇒ a3 + b3 + c3 - 3abc = (6)[40 - (-2)]
⇒ a3 + b3 + c3 - 3abc = 6 × 42
⇒ a3 + b3 + c3 - 3abc = 252
Therefore, the value of a³ + b³ + c³ - 3abc is 252.
Last updated on Jul 22, 2025
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