Question

. If x + y +z =0, what is the value of x^2/yz + y^2/xz+ z^2/xy ?

Answer 1

$x + y + z = 0$

Therefore,

$\frac{ {x}^{2} }{yz} + \frac{ {y}^{2} }{xz} + \frac{ {z}^{2} }{xy}$

$= \frac{ {x}^{3} + {y}^{3} + {z}^{3} }{xyz}$

Now,

$x + y + z = 0$

Therefore,

${x}^{3} + {y}^{3} + {z}^{3} = 3xyz$

Therefore,

$\frac{ {x}^{3} + {y}^{3} + {z}^{3} }{xyz}$

$= \frac{3xyz}{xyz}$

$= 3$