If ⁻¹ x+ ⁻¹(1-x)= ⁻¹ x , then x to

Step-by-step solution

We have, aligned & ⁻¹ x+ ⁻¹(1-x)= ⁻¹ x & ⁻¹(1-x)= 2 - ⁻¹ x- ⁻¹ x & = 2 -2 ⁻¹ x & [ ⁻¹ x+ ⁻¹ x= 2 ] & ⁻¹(1-x)= ⁻¹ 1- ⁻¹ 2 x 1-x^2 & ⁻¹(1-x)= ⁻¹ (1 1-4 x^2 (1-x^2 ) -0 ) & (1-x)= 1-4 x^4+4 x^2 = (1-2 x^2 )^2 & (1-x)=1-2 x^2 & 2 x^2-x=0 & x(2 x-1)=0 & x=0, 1 2 & x 0, 1 2 aligned