If ( ⁻¹ x )= ⁻¹ ( a b^2-a^2 ) b a , then x =

Step-by-step solution

Given that, ( ⁻¹ x )= ⁻¹ ( a b^2-a^2 ) Since, ⁻¹ x= ⁻¹ ( x 1-x^2 ) and ⁻¹ x= ⁻¹ ( 1+x^2 ) ( ⁻¹ x 1-x^2 )= ⁻¹ 1+ ( a b^2-a^2 )^2 x 1-x^2 = b^2-a^2+a^2 b^2-a^2 x 1-x^2 = b b^2-a^2 On squaring both the sides, we get x^2 1-x^2 = b^2 b^2-a^2 aligned & x^2 b^2-x^2 a^2=b^2-b^2 x^2 & x^2 b^2+b^2 x^2-x^2 a^2=b^2 aligned 2 x^2 b^2-x^2 a^2=b^2 x^2 (2 b^2-a^2 )=b^2 x= b 2 b^2-a^2