If the roots of the equation (a-1) (x^2+x+1 )^2=(a+1) (x^4+x^2+1 ) are real and distinct then the value of a

Step-by-step solution

x^4+x^2+1= (x^2+1 )^2-x^2= (x^2+x+1 ) (x^2-x+1 )x^2+x+1= (x+ 1 2 )^2+ 3 4 0 aligned Now, (a-1) (x^2+x+1 )^2 & =(a+1) (x^4+x^2+1 ) (a-1) (x^2+x+1 ) & =(a+1) (x^2-x+1 ) aligned x^2-a x+1=0 which has real and distinct roots array ll & =a^2-4 0 & a^2 4 & a (- ,-2) (2, ) array