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Question
If `x = (sqrt(2a + 1) + sqrt(2a - 1))/(sqrt(2a + 1) - sqrt(2a - 1))`, then which of the following is true?
Options
x2 + 2ax + 1 = 0
x2 – 2ax + 1 = 0
x2 + 4ax – 1 = 0
x2 – 4ax + 1 = 0
MCQ
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Solution
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.
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