Question : If $x+\frac{1}{x}=2$, then the value of $x^{11}+\frac{1}{x^{20}}$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 7
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Correct Answer: 2
Solution :
Given, $x+\frac{1}{x}=2$
⇒ $x^2+1=2x$
⇒ $x^2+1-2x=0$
⇒ $(x-1)^2=0$
⇒ $x-1=0$
$\therefore x=1$
Consider, $x^{11}+\frac{1}{x^{20}}$
= $1^{11}+\frac{1}{1^{20}}$
= $1+1$
= $2$
Hence, the correct answer is 2.
Related Questions
Question : If $x+\frac{1}{x}=-2$, then what is the value of $x^7+x^{-7}+x^2+x^{-2} ?(\mathrm{x}<0)$
Question : If $\frac{x}{y}=\frac{4}{5}$, then the value of $(\frac{4}{7}+\frac{2y–x}{2y+x})$ is:
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