Question
Download Solution PDFIf a + b + c = 7, ab + bc + ca = 11 and abc = −1, then a3 + b3 + c3 is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
a + b + c = 7, ab + bc + ca = 11 and abc = −1
Formula used:
a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2+ c2 - ab - bc - ca)
(a + b + c)2 = (a2 + b2+ c2 + 2ab + 2bc + 2ca)
Calculation:
(a2 + b2+ c2) = (a + b + c)2 - 2ab + 2bc + 2ca
⇒ (a2 + b2+ c2) = 49 - 22
⇒ (a2 + b2+ c2) = 27
So,
a3 + b3 + c3 - 3abc = 7× (27 - 11)
⇒ a3 + b3 + c3 - 3abc = 112
⇒ a3 + b3 + c3 = 112 - 3
⇒ a3 + b3 + c3 = 109
∴ The correct option is 3
Last updated on Jun 25, 2025
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