Question 38

If $$(\frac{x}{y})+(\frac{y}{x})=1$$, then what is the value of $$x^3 + y^3$$ ?

Solution

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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