Question 86

If $$\dfrac{x^{2}}{yz}+\dfrac{y^{2}}{zx}+\dfrac{z^{2}}{xy}=3$$, then what is the value of $$(x+y+z)^{3}$$ ?

Solution

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

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

=> $$x^3+y^3+z^3=3xyz$$

=> $$x^3+y^3+z^3-3xyz=0$$

=> $$(x+y+z)(x^2+y^2+z^2-xy-yz-zx)=0$$

=> $$x+y+z=0$$

Cubing both sides, we get :

=> $$(x+y+z)^3=0$$

=> Ans - (A)

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