(A) Given the equation $x+\frac{1}{x}=2$.Multiplying both sides by $x$,we get $x^2+1=2x$,which simplifies to $x^2-2x+1=0$.This is a perfect square: $(

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(A) Given the equation $x+\frac{1}{x}=2$.Multiplying both sides by $x$,we get $x^2+1=2x$,which simplifies to $x^2-2x+1=0$.This is a perfect square: $(x-1)^2=0$,which implies $x=1$.Now,substitute $x=1$ into the expression $x^{100}+\frac{1}{x^{100}}$:$1^{100}+\frac{1}{1^{100}} = 1+1 = 2$.Therefore,the value is $2$.

Competitive Quantitative Aptitude Number system Simplification

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If $x+\frac{1}{x}=2,$ then the value of $x^{100}+\frac{1}{x^{100}}$ is

A
$2$
B
$0$
C
$1$
D
$-2$

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If $x+\frac{1}{x}=2,$ then the value of $x^{100}+\frac{1}{x^{100}}$ is

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If $N = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}},$ then what is the value of $N + \frac{1}{N} ?$

$3 \frac{3}{4} + 4 \frac{2}{5} - 3 \frac{1}{8} = ?$

What will come in place of the question mark (?) in the following equation?$4003 \times 77 - 21015 = ? \times 116$

$\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$ is approximately equal to

When $52416$ is divided by $312,$ the quotient is $168.$ What will be the quotient when $52.416$ is divided by $0.0168?$

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What will come in place of the question mark (?) in the following equation?
$4003 \times 77 - 21015 = ? \times 116$