JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(x\) is a solution of the equation, \(\sqrt {2x + 1} - \sqrt {2x - 1} = 1, \left( {x \ge \frac{1}{2}} \right)\) , then \(\sqrt {4{x^2} - 1} \) is equal to
- A \(\frac{3}{4}\)
- B \(\frac{1}{2}\)
- C \(2\sqrt 2 \)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(\sqrt{2 x+1}-\sqrt{2 x-1}=1..........(1)\) \(\Rightarrow \quad 2 x+1+2 x-1-2 \sqrt{4 x^{2}-1}=1\) \(\Rightarrow 4 x-1=2 \sqrt{4 x^{2}-1}\) \(\Rightarrow 16 x^{2}-8 x+1=16 x^{2}-4\) \(\Rightarrow 8 x=5\) \(\Rightarrow \quad x=\frac{5}{8}\) which satisfies equation \((1)\) So,…
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