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If a+b+c=5 and ab+bc+ca=10, then prove t...

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

Text Solution

Verified by Experts

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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