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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`.

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To prove that \( a^3 + b^3 + c^3 - 3abc = -25 \) given \( a + b + c = 5 \) and \( ab + bc + ca = 10 \), we can use the identity: \[ a^3 + b^3 + c^3 - 3abc = (a + b + c) \left( (a + b + c)^2 - 3(ab + bc + ca) \right) \] ### Step 1: Substitute the known values into the identity We know: ...
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