Question

If `x = (sqrt(2a + 1) + sqrt(2a - 1))/(sqrt(2a + 1) - sqrt(2a - 1))`, then which of the following is true?

विकल्प

• x² + 2ax + 1 = 0

• x² – 2ax + 1 = 0

• x² + 4ax – 1 = 0

• x² – 4ax + 1 = 0

Answer 1

x² – 4ax + 1 = 0

Explanation:

Applying componendo and dividendo gives `(x + 1)/(x - 1) = sqrt((2a + 1)/(2a - 1))`.

Squaring and simplifying gives x² – 4ax + 1 = 0.