Question

if x+y+z=0 then show that x^2/yx+y^2/xz+z^2/yx=3​

Answer 1

Answer:

See the explanation

Step-by-step explanation:

Given  $x+y+z=0$

To prove

         $\dfrac{x^2}{yz}+\dfrac{y^2}{zx}+\dfrac{z^2}{xy}=3$

We know that, If $x+y+z=0$, then $x^3+y^3+z^3=3xyz$ ...(1)

Now

            $\text{LHS}=\dfrac{x^2}{yz}+\dfrac{y^2}{zx}+\dfrac{z^2}{xy}$

                     $=\dfrac{x^3+y^3+z^3}{xyz}$, taking LCM and simplifying

                     $=\dfrac{3xyz}{xyz}=3=\text{RHS}$ using (1)

Hence proved