If a+b+c =9 and a² + b²+ c²=35 find the value of a³ + b³ + c³ - 3ab

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Solution

(a+b+c)²=9²=81
a²+b²+c²+2ab+2bc+2ca=81
a²+b²+c²+2ab+2bc+2ca-(a²+b²+c²)=81-35
2ab+2bc+2ca=46
2(ab+bc+ca)=46
(ab+bc+ca)=23
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
=9(35-(ab+bc+ca))
=9(35-23)
=9(12)=108

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If a + b + c = 9, and $a^{2} + b^{2} + c^{2} = 35$ , find the value of $a^{3} + b^{3} + c^{3} - 3 a b c .$

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a^{3} + b^{3} + c^{3} = 3 a b c a n d a + b + c = 0

\frac{(b + c)^{2}}{3 b c} + \frac{(c + a)^{2}}{3 a c} + \frac{(a + b)^{2}}{3 a b} =

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