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  • If a, b, c are all non-zero and a + b + c = 0, prove that \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}=3

If a, b, c are all non-zero and a + b + c = 0, prove that \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}=3

Answers (1)

Given, \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}=3

L.H.S. \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}

Taking LCM of denominators, we get

L.H.S \frac{a^{3}+b^{3}+c^{3}}{abc}

Now we know that if a + b + c = 0 then a^{3}+b^{3}+c^{3}=3abc

Putting the value in above equation:

 L.H.S = \frac{3abc}{abc} = 3 = RHS

Hence proved.

Posted by

infoexpert24

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