if `a`, and `c` are all non zero and `a+b+c=0` , then find the value of `(a^(2))/(bc)+(b^(2))/(ac)+(c^(2))/(ab)`

Options

A. 2
B. -2
C. 3
D. -3

Answer

C

Explanation

to prove `(a^(2))/(bc)+(b^(2))/(ac)+(c^(2))/(ab)=3.`
we know that ,` a^(3)+b^(3)+c^(3)-3abc=(a^(2) +b^(2) +c^(2) -aab-bc -ca)`
`=0(a^(2) +b^(2)+c^(2)-ab-bc-ca)[ :' a+b+c=0,"given "]`
`=0`
`implies a^(3)+b^(3)+c^(3)=3abc`
on dividing both sides by abc , we get
`(a^(3))/(abc)+(b^(3))/(abc)+(c^(3))/(abc)=3.`
`implies (a^(2))/(bc)+(b^(2))/(ac)+(c^(2))/(ab)=3.`