Question

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

Answer 1

We have to find the value of  `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)`

Put  `a+b +c = 0`

 `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 axx a)/(abc) +(b xx bxx b)/(abc) +(c xx cxx c)/(abc) =3`

                                  `a^2/bc +b^2/ac +c^2 /ab=3`

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