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Question

If a+b+c=9 then find the value of
(3a)3+(3b)3+(3c)33(3a)(3b)(3c)

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Solution

Given that,
a+b+c=9
(3a)3+(3b)3+(3c)33(3a)(3b)(3c)
=(3a+3b+3c)(3a)2+(3b)2+(3c)2(3a)(3b)(3b)(3c)(3c)(3a)
|9(a+b+c)|(3a)2+(3b)2+(3c)2(3a)(3b)(3b)(3c)(3c)(3a)
(99)(3a)2+(3b)2+(3c)2(3a)(3b)(3b)(3c)(3c)(3a)
0(3a)2+(3b)2+(3c)2(3a)(3b)(3b)(3c)(3c)(3a)
=0


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