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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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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Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?
Question : If $2x-\frac{2}{x}=1(x \neq 0)$, then the the value of $(x^3-\frac{1}{x^3})$ is:
Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:
Question : If $2x+\frac{2}{x}=3$, then the value of $x^{3}+\frac{1}{x^{3}}+2$ is:
Question : If $\frac {x^2+3x+1}{x^2–3x+1}=\frac{1}{2 }$, then the value of $(x+\frac{1}{x})$ is:
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