Question : If $\frac{x}{8}+\frac{8}{x}=1$, then the value of $x^3$ is:
Option 1: – 256
Option 2: – 512
Option 3: 256
Option 4: 512
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Answer (1)
22nd Jan, 2024
Correct Answer: – 512
Solution :
Given, $\frac{x}{8}+\frac{8}{x}=1$
⇒ $x^2+64=8x$
⇒ $x^2-8x+64=0$
⇒ $(x+8)(x^2-8x+64)=0$
⇒ $(x^3+8^3)=0$
⇒ $x^3=-512$
Hence, the correct answer is – 512.
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