If k is a root of x^2 - 4x + 1 = 0 , then what is ⁻¹k + ⁻¹ 1 k equal to?

Step-by-step solution

The given equation is x^2 - 4x + 1 = 0 . The roots of the equation are given by x = 4 16 - 4 2 = 2 3 . Since 3 1.732 , both roots 2 + 3 and 2 - 3 are positive. Therefore, k > 0 . Using the standard inverse trigonometric identity for x > 0 : ⁻¹x + ⁻¹ ( 1 x ) = 2 Substituting x = k , we get: ⁻¹k + ⁻¹ ( 1 k ) = 2 Answer: 2