Question

if x+1/x = 2 find x99 + 1/x99

Answer 1

since x=1,

therefore
x99+1/x99 =2

Answer 2

Given,

x+1/x = 2

To find,

The value of x^99 + (1/x)^99

Solution,

We can simply solve this mathematical problem using the following process:

According to the question;

x+1/x = 2

=> (x^2 + 1)/x = 2

=> (x^2 + 1) = 2x

=> x^2 - 2x + 1 = 0

=> (x)^2 + (1)^2 - 2(1)(x) = 0

=> (x-1)^2 = 0

{using the identity: (a-b)^2 = a^2 + b^2 -2ab}

=> x-1 = 0

=> x = 1

So, the value of x^99 + (1/x)^99

= x^99 + (1/x)^99

= (1)^99 + (1/1)^99

= (1)^99 + (1)^99

= 1+1 = 2

Hence, the value of x^99 + (1/x)^99 is equal to 2.