Question

Please Help Me Out

(x+ 1/x)^2 = 4+3/2(x- 1/x)

Answer 1

$\fontsize{18}{10}{\textup}{\textbf{The required root is 2}}}$

Step-by-step explanation:

(x+ 1/x)^2 = 4+3/2(x- 1/x)

=>x^2+1/x^2+2*x*1/x=4+3/2(x-1/x)

=>x^2+1/x^2-2*x*1/x+4*x*1/x=4+3/2(x-1/x)

=>(x-1/x)^2+4=4+3/2(x-1/x)

=>(x-1/x)^2=3/2(x-1/x)

Either, x+1/x=0                                          or, x+1/x=3/2

=>x^+1=0                                                     =>2x^2-3x+2=0

=>x=sqrt(-1), imaginary                               =>(2x-1)(x-2)=0

                                                                   =>x=1/2 or2

The value 1/2 does not satisfy the original equation, so the only real root is 2