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Inverse of a Matrix

If a+b+c=0 ...

Question

If $a + b + c = 0$ then find the value of $a^{3} + b^{3} + c^{3}$ .

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Solution

Given,
$a + b + c = 0$
or, $a + b = - c$ ......(1).
Now cubing both sides we get,
$(a^{3} + b^{3} + 3 a b (- c) = - c^{3}$ [ Using (1)]
or, $a^{3} + b^{3} + c^{3} = 3 a b c$ .

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a + b + c = 0

, then the value of

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a + b + c = 0

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> 0

, then prove that

\frac{a^{3}}{b^{3}} + \frac{b^{3}}{c^{3}} + \frac{c^{3}}{a^{3}} \geq 3

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(a + b - c)^{3} + (b + c - a)^{3} + (c + a - b)^{3}

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then find the value of

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