Question

x+1/x=2,then find x100-1/x100

Answer 1

We have:

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

If $x+\dfrac{1}{x}$ = 2, then find the value of $x^{100} -\dfrac{1}{x^{100}}$ is:

Solution"

∴ $x+\dfrac{1}{x}$ = 2

Put x = 1, we get

$1+\dfrac{1}{1}$ = 2

⇒ 1 + 1 = 2

⇒ 2 = 2,x = 1 is satisfied.

∴ $x^{100} -\dfrac{1}{x^{100}}$

Put x = 1 , we get

$1^{100} -\dfrac{1}{1^{100}}$

= $1-\dfrac{1}{1}$

= 1 - 1

= 0

∴ $x^{100} -\dfrac{1}{x^{100}}$ = 0

Thus, If $x+\dfrac{1}{x}$ = 2, then find the value of $x^{100} -\dfrac{1}{x^{100}}$ is equal to zero(0).

Answer 2

SOLUTION

GIVEN

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

TO DETERMINE

$\displaystyle \sf{ {x}^{100} - \frac{1}{ {x}^{100} } }$

EVALUATION

Here the it is given that

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

$\displaystyle \sf{ \implies \:\frac{ {x}^{2} + 1}{x} = 2}$

$\displaystyle \sf{ \implies \: {x}^{2} + 1 = 2x}$

$\displaystyle \sf{ \implies \: {x}^{2} - 2x+ 1 = 0}$

$\displaystyle \sf{ \implies \: {(x - 1)}^{2} = 0}$

$\displaystyle \sf{ \implies \: x = 1}$

Now

$\displaystyle \sf{ {x}^{100} - \frac{1}{ {x}^{100} } }$

$\displaystyle \sf{ = {(1)}^{100} - \frac{1}{ {(1)}^{100} } }$

$= 1 - 1$

$= 0$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If x+1/x=3 then, x^7+1/x^7=

https://brainly.in/question/23295932

2. if 3√x+(3√3375) ^3 =17 , then find the cube root of x-1026 is equal to

https://brainly.in/question/28465037