What is the value of $a^{3} + b^{3} + c^{3} - 3 abc if a + b + c = 12 and ab + bc + ca = 47$

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Solution

The correct option is B 36
Solution :-

Given $a + b + c = 12$ and $a b + b c + c a = 47$

We know,

$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$

$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - (a b + b c + c a))$

Now,

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)$

$144 = a^{2} + b^{2} + c^{2} + 94$

$\Rightarrow a^{2} + b^{2} + c^{2} = 50$

$∴ a^{3} + b^{3} + c^{3} - 3 a b c = 12. (50 - 47)$

$a^{3} + b^{3} + c^{3} - 3 a b c = 36$

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Similar questions

If $a + b + c = 8$ and $a b + b c + c a = 20$ , the value of $a^{3} + b^{3} + c^{3} - 3 a b c$ is ___

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a^{3} + b^{3} + c^{3} - 3 a b c ?

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a^{3} + b^{3} + c^{3} - 3abc

If $a + b + c = 8$ and $a b + b c + c a = 20$ , find the value of $a^{3} + b^{3} + c^{3} - 3 a b c$ .

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