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If a+b+c=9 and a^2+b^2+c^2=35, find the ...

If `a+b+c=9` and `a^2+b^2+c^2=35`, find the value of `(a^3+b^3+c^3-3abc)`.

Text Solution

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`(a+b+c)=9rArr (a+b+c)^2=81`
`rArr (a^2+b^2+c^2)+2(ab+bc+ca)=81`
`rArr 35+ 2(ab+bc+ca)=81rArr (ab+bc+ca)=23`
` therefore (a^3+b^3+c^3-abc)=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)`
` =(a+b+c)[(a+b+c)^2 -3(ab+bc+ca)]`.
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