If the roots of the equation (a−1)x2+x+12=(a+1)x4+x2+1 are real and distinct then the value of a∈

x4+x2+1=x2+12−x2=x2+x+1x2−x+1x2+x+1=x+122+34≠0 ∀ real xTherefore we can cancel this factor and we get  a-1x2+x+1=a+1x2-x+1ax2+x+1-x2+x-1=x2-x+1+x2+x+1 a2x=2x2+2x2-ax+1=0  x2−ax+1=0 has real and distinct roots ⇒ D=a2−4>0⇒a∈(−∞,−20)∪(2,∞)