यदि `x+y+z=0` है तो `(x^(2))/(yz)+(y^(2))/(zx)+(z^(2))/(xy)=?`

Options

A. `(xyz)2`
B. `x^(2)+y^(2)+z^(2)`
C. `9`
D. `3`

Answer

D

Explanation

`(x^(2))/(yz)+(y^(2))/(zx)+(z^(2))/(xy)`
`=(x^(2))/(yz)xx x/x +(y^(2)xxy)/(zx xxy)+(z^(2))/(xy)xx z/z`
`= (x^(3)+y^(3)+z^(3))/(xyz)`
`( :.` If `x+y+z=0` then `x^(3)+y^(3)+z^(3)implies3xyz)`
`:.(3xyz)/(xyz)=3`