Question

If x + 1 upon x = 4 then find the value of x square + 1 upon x square?

Answer 1

`x^2+1/x^2=14`

Explanation:

As `x+1/x=4`, squaring it we get

`x^2+2xx x xx 1/x+(1/x)^2=16`

or `x^2+2+1/x^2=16`

and hence `x^2+1/x^2=16-2=14`

Answer 2

Considering a different method...
Use complex numbers

Explanation:

Let `cos theta + i sin theta = x`

Using de moivres theorem you can yield:

`=> x + 1/x = 2cos theta " and " x^2 + 1/x^2 = 2cos2theta`

`=> 2cos theta = 4`

`=> cos theta = 2`

`=> cos2theta = 2cos^2 theta -1`

`=> cos2theta = 2 ( 2^2 ) - 1`

`=> cos2theta = 7 => 2cos2theta = 14`

`=> x^2 +1/x^2 = 14`

This method is good for questions like:

`x + 1/x = a` then find `x^3 + 1/x^3`

Using de moivres:

`x^3 +1/x^3 = a^3 - 3 a`