If ⁻¹ x^2+x + ⁻¹ x^2+x+1 = 2 , then the value of x is

Step-by-step solution

aligned & ⁻¹ x^2+x + ⁻¹ x^2+x+1 = 2 & ⁻¹ x^2+x = 2 - ⁻¹ x^2+x+1 = ⁻¹ x^2+x+1 & ⁻¹ x^2+x = ⁻¹ - (x^2+x ) x^2+x+1 ; - (x^2+x ) & x^2+x= - (x^2+x ) x^2+x+1 & (x^2+x ) (x^2+x+1 )=- (x^2+x ) [ let x^2+x=y ] & y(y+1)=-y & y^2+2 y=0 & y(y+2)=0 & y=0 or y=-2 & x^2+x=0 or x^2+x=-2 & x(x+1)=0 or x^2+x+2=0 & (x=0,-1) or (No solution) aligned