Question

please explain me how this is solved step 4 doubt ....step 4 from starting . please help

Answer 1

hope you will understand now..

Answer 2

In step 4, they have used the basic identity.

(a+b)² = a² + b² +2ab

in the step 3 they have calculated (a+b)², ie the LHS of the identity.
and in step 4 they have calculated the RHS of the Identity, ie, a² + b² + 2ab

if you take,
a= x and
b = 1/x
the identity will be formed as follows:

(x+ 1/x)² = x² + 1/x² +2×x×1/x

(x+ 1/x)² = x² + 1/x² +2

(x+ 1/x)² - 2 = x² + 1/x²

x² +1/x² = (x + 1/x)² - 2

They have calculated (x + 1/x) and substituted here and thus you will get the value of x² +1/x²

I hope you understand the approach.
All the best!