If $$\frac{a}{b}+\frac{b}{a}=1$$, then the value of $$a^3+b^3$$ isÂ
Given : $$\frac{a}{b}+\frac{b}{a}=1$$
=> $$\frac{a^2+b^2}{ab}=1$$
=> $$a^2+b^2=ab$$ -----------(i)
We know that, $$(a^3+b^3)=(a+b)(a^2+b^2-ab)$$
Substituting value from equation (i), we get :
=> $$(a^3+b^3)=(a+b)(ab-ab)$$
=> $$(a^3+b^3)=(a+b) \times 0=0$$
=> Ans - (B)
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