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  4. The equation √x+1-√x-1=√4x-1 has

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Q. The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has

IIT JEEIIT JEE 1997Complex Numbers and Quadratic Equations

Solution:

Since, $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$
$\Rightarrow (x+1)+(x-1)-2\sqrt{x^2-1}=4x-1$
$\Rightarrow 1-2x=2\sqrt{x^2-1}$
$\Rightarrow 1+4x^2-4x=4x^2-4$
$ 4x=5 \Rightarrow x=\frac{5}{4}$
But it does not satisfy the given equation. Hence, no solution exists.