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Question:
The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has
The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has
Updated On: Jul 29, 2023
- no solution
- one solution
- two solutions
- more than two solutions
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The Correct Option is A
Solution and Explanation
Since, $\hspace25mm\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$
$\Rightarrow\, \, \, \, \, \, (x+1)+(x-1)-2\sqrt{x^2-1}=4x-1$
$\Rightarrow\hspace25mm1-2x=2\sqrt{x^2-1}$
$\Rightarrow\, \, \, \, \, \, 1+4x^2-4x=4x^2-4$
$\hspace25mm 4x=5 \Rightarrow x=\frac{5}{4}$
But it does not satisfy the given equation.
Hence, no solution exists.
$\Rightarrow\, \, \, \, \, \, (x+1)+(x-1)-2\sqrt{x^2-1}=4x-1$
$\Rightarrow\hspace25mm1-2x=2\sqrt{x^2-1}$
$\Rightarrow\, \, \, \, \, \, 1+4x^2-4x=4x^2-4$
$\hspace25mm 4x=5 \Rightarrow x=\frac{5}{4}$
But it does not satisfy the given equation.
Hence, no solution exists.
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