Question

if x^4-x^2+1=0 then find the value of x2+1/x^2?

Answer 1

x^4 - x^2 + 1 = 0

     Adding - 1 on both sides :

x^4 - x^2 + 1 - 1 = - 1

x^4 - x^2 = - 1

     

Taking x^2 common in x^4 - x^2

     

x^2( x^2 - 1 ) = - 1

Dividing by x^2 on both sides :

x^2( x^2 - 1 ) / x^2  = - 1 / x^2

x^2 - 1 = - 1 / x^2

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

x^2 + 1 / x^2 = 1

Therefore, the value of x^2 + 1 / x^2 is 1 .