The number of real solutions of the equation ⁻¹ x(x+1) + ⁻¹ x²+x+1 = 2 is

Step-by-step solution

Given, ⁻¹ x(x+1) + ⁻¹ x²+x+1 = 2 ⁻¹ 1 (x²+x )²+1 = 2 - ⁻¹ x ²+ x +1 ⁻¹ 1 (x²+x )²+1 = ⁻¹ x²+x+1 1 (x²+x )²+1 = x²+x+1 1= (x²+x+1 ) [ (x²+x )²+1 ] ( x ²+ x )³+ ( x ²+ x )²+ ( x ²+ x )+1=1 (x²+x ) [ (x²+x )²+ (x²+x )+1 ]=0 x²+x=0 x =0,-1 Hence, both values of x satisfies the given equation.