If `a+b+c=5` and `ab+bc+ca=10`, then prove that `a^3+b^3+c^3-3abc=-25`

1.	If `a+b+c=5` and `ab+bc+ca=10`, then prove that `a^3+b^3+c^3-3abc=-25`.
Answer» We have `(a^3+b^3+c^3-3abc)=(a+b+c)(a62+b^2+c^2-ab-bc-ca)` `=(a+b+c)[(a+b+c)^2-3(ab+bc+ca)]` `=5xx [(5)^2-(3xx10)]` `=5xx(25-30)=5xx(-5)=-25` Hence , `(a^3+b^3+c^3-3abc)=-25`.

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