If ( 2 ⁻¹ 3 10 + ⁻¹x ) = 2 , where x > 0 , then the value of x^2 is:

Step-by-step solution

Let us first simplify the term 2 ⁻¹ 3 10 . Let ⁻¹ 3 10 = . Then = 3 10 , which gives = 1 3 . So, 2 ⁻¹ 3 10 = 2 ⁻¹ 1 3 . Using the double angle formula 2 ⁻¹y = ⁻¹ ( 2y 1-y^2 ) , we get: 2 ⁻¹ 1 3 = ⁻¹ ( 2(1/3) 1 - (1/3)^2 ) = ⁻¹ ( 2/3 8/9 ) = ⁻¹ 3 4 . Now, let ⁻¹x = . Then = x , and = 1 x^2-1 . The given equation becomes: ( ⁻¹ 3 4 + ) = 2 Using the tangent addition formula (A+B) = A + B 1 - A B : 3 4 + 1 - 3 4 = 2 3 4 + = 2 (1 - 3 4 ) 3 4 + = 2 - 3 2 + 3 2 = 2 - 3 4 5 2 = 5 4 = 1 2 Since = 1 x^2-1 , we have: 1 x^2-1