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Expansion of (x^2 - y^2)

If, a+b+c=11,...

Question

If,a+b+c=11,abc=12,ab+bc+ca=36,then find the value of a³+b³+c³

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Solution

(a+b+c) ³= a³+b³+c³+3[(a+b+c)(ab+bc+ca) - abc]
11³=a³+b³+c³+3[11*36 - 12]
1331=a³+b³+c³+3(384)
a³+b³+c³=1331-1152
=179

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