Question

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

Answer 1

ANSWER:  roots are imaginary

Step-by-step explanation:

let x+1/x =A

then the equation becomes,  A^2=3A+4

it is in the form of quadratic equation then

A^2-3A-4=0

A^2-4A+A-4=0

A(A-4)+1(A-4)=0

(A-4)(A+1)=0

now A-4=0  ,  A+1=0

        A=4    ,   A=-1

we know  A=x+1/x

        x+1/x=4

      (x^2+1)=4x

     b^2-4ac is less than 0

hence it has imaginary roots

  x=2±√3

       we know A=-1

  x+1/x=-1

x^2+1=-x

it has imaginary roots

x=-1/2 ±(√-3)/2