Question

if a+b+c=6 and a^2+b^2+c^2=12 find a^3+ b^3 +c^3

Answer 1

Answer:

a+b+c= 6 and a ^2 + b^ 2 +c ^ 2 = 12,  

Consider the formula - a³+b³+c³- 3abc = (a+b+c) (a²+b²+c²-(ab+bc+ca))

We have to find ab+bc+ca

given a+b+c = 6

Squaring on both sides we get,

(a+b+c)² = 6²

a²+b²+c² + 2(ab+bc+ca) = 36

2 (ab+bc+ca) = 24

ab + bc + ca = 12

Now, a³+b³+c³-3abc = (a+b+c) (a²+b²+c²-(ab+bc+ca))

a³+b³+c³ =(a+b+c) (a²+b²+c²-(ab+bc+ca)) + 3abc

             = 6 ( 12 - 12 ) + 3 abc

             = 3abc ( answer )

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