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SOLUTION
GIVEN
a + b + c = 6
ab + bc + ca = 11
TO FIND VALUE OF
a^3 + b^3 + c^3 - 3abc
EXPLANATION
a + b + c = 6
(a + b + c) ^2 = 36
a^2 + b^2 + c^2 + 2 ( ab + bc + ca) = 36
a^2 + b^2 + c^2 + 2 ( 11) = 36
a^2 + b^2 + c^2 = 14
FORMULA OF a^3 + b^3 + c^3 - 3abc
( a + b + c) ( a^2 + b^2 + c^2 - ab - bc - ca)
( a + b + c) [ a^2 + b^2 + c^2 - (ab + bc + ca) ]
6 X (14 - 11 )
6 X 3 = 18
therefore,
a^3 + b^3 + c^3 - 3abc = 18
ANSWER = 18
FORMULA USED
- ( a + b + c)^2 =
a^2 + b^2 + c^2 + 2 ( ab + bc + ca)
- a^3 + b^3 + c^3 - 3abc =
( a + b + c) [ a^2 + b^2 + c^2 - ab - bc - ca]
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