Question

x+1/x=2 then x10+1/x10=

Answer 1

x+1/x=2
Then
(x+1/x)^2=2^2
x^2+2×x×1/x+1/x^2=4
x^2+2+1/x^2=4
x^2+1/x^2=2
x+1/x=x^2+1/x^2
That means x=1.
10x+1/10x=2

Answer 2

Answer:

$ans. \: \: \: \huge \boxed {\: \bold \green {2}}$

Step-by-step explanation:

$x + \frac{1}{x} = 2$

$\frac{ {x}^{2} + 1}{x} = 2$

${x}^{2} + 1 = 2x$

${x}^{2} - 2x + 1 = 0$

$(x - 1)^{2} = 0$

$x - 1 = 0$

$x = 1$

Now,

Substitute the value of x,

${x}^{10} + \frac{1}{ {x}^{10} } = {1}^{10} + \frac{1}{ {1}^{10} } = 1 + 1 = 2$