Question : If $\frac{x}{3}+\frac{3}{x}=1$, then the value of $x^3$ is:
Option 1: 1
Option 2: 27
Option 3: 0
Option 4: –27
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Correct Answer: –27
Solution : Given: $\frac{x}{3}+\frac{3}{x}=1$ ⇒ $\frac{x^2+9}{3x}=1$ ⇒ $x^2+9=3x$ ⇒ $x^2-3x+9=0$ ⇒ $(x+3)(x^2-3x+9)=(x+3)×0$ [Multiplying both sides by $(x+3)$] ⇒ $x^3+3^3=0$ (Applying formula) ⇒ $x^3=-(3)^3$ ⇒ $x^3=-27$ Hence, the correct answer is –27.
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