aligned & If ( ⁻¹ x )= ⁻¹ ( a b^2-a^2 ) : & b>a, then x = aligned

Step-by-step solution

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