Theory of Equations 1 Question 29
30. The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4 x-1}$ has
(1997C, 2M)
(a) no solution
(b) one solution
(c) two solutions
(d) more than two solutions
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Solution:
- Since,
$$ \sqrt{x+1}-\sqrt{x-1}=\sqrt{4 x-1} $$
$\Rightarrow \quad(x+1)+(x-1)-2 \sqrt{x^{2}-1}=4 x-1$
$\Rightarrow \quad 1-2 x=2 \sqrt{x^{2}-1} \Rightarrow 1+4 x^{2}-4 x=4 x^{2}-4$
$\Rightarrow \quad 4 x=5 \quad \Rightarrow \quad x=\frac{5}{4}$
But it does not satisfy the given equation.
Hence, no solution exists.
