1. If $$\frac{x^{2}}{yz}+\frac{y^{2}}{zx}+\frac{z^{2}}{xy}=3$$, then what is the value of $$(x+y+z)^{3}$$ ?
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By: anil on 05 May 2019 02.55 pm
Given : $$frac{x^{2}}{yz}+frac{y^{2}}{zx}+frac{z^{2}}{xy}=3$$ => $$frac{x^3+y^3+z^3}{xyz}=3$$ => $$x^3+y^3+z^3=3xyz$$ => $$x^3+y^3+z^3-3xyz=0$$
=> $$(x+y+z)(x^2+y^2+z^2-xy-yz-zx)=0$$ => $$x+y+z=0$$ Cubing both sides, we get : => $$(x+y+z)^3=0$$ => Ans - (A)
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=> $$(x+y+z)(x^2+y^2+z^2-xy-yz-zx)=0$$ => $$x+y+z=0$$ Cubing both sides, we get : => $$(x+y+z)^3=0$$ => Ans - (A)