1. If $$(\frac{x}{y})+(\frac{y}{x})=1$$, then what is the value of $$x^3 + y^3$$ ?
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By: anil on 05 May 2019 02.55 pm
Given : $$frac{x}{y}+frac{y}{x}=1$$ => $$frac{x^2+y^2}{xy}=1$$ => $$x^2+y^2=xy$$ -----------(i) We know that, $$(x^3+y^3)=(x+y)(x^2+y^2-xy)$$ Substituting value from equation (i), we get : => $$(x^3+y^3)=(x+y)(xy-xy)$$ => $$(x^3+y^3)=(x+y) imes 0=0$$ => Ans - (B)
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