Question

If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]

Options

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Answer 1

We have to find  `a^2/(bc)+ b^2 /(ca) +c^2 /(ab)`

Given  a + b + c = 0

Using identity   `a^3 +b^3 +c^3 -3abc = (a+b+c)(a^2 +b^2 +c^2 -ab -bc -ca)`

`a^3 +b^3 +c^3 -3abc = 0 (a^2 +b^2 +c^2 -ab -bc -ca)`

`a^3 +b^3 +c^3 - 3abc = 0 `

                  `a^3 +b^3 + c^3 = 3abc`

                                                  `a^3 /(abc)+ b^3/(abc) +c^3 /(abc ) = 3`

`((a xx a xx a)/(a xx b xx c))+ ((b xx b xx b)/(a xx b xx c))+((c xx c xx c)/(a xx b xx c)) = 3 `

                                                  `a^2 /(abc)+ b^2/(abc) +c^2 /(abc ) = 3`

Hence the value of   `a^2 /(bc)+ b^2/(ac) +c^2 /(ab ) = 3`.