If $$(\frac{x}{y})+(\frac{y}{x})=1$$, then what is the value of $$x^3 + y^3$$ ?
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 :
=> $$(x^3+y^3)=(x+y)(xy-xy)$$
=> $$(x^3+y^3)=(x+y) \times 0=0$$
=> Ans - (B)
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