| Statement-1: Given equation has no solution |
| Statement-2: \[x=\frac{5}{4}\]is an extraneous solution of given equation. |
A) Statement -1 is true, statement -2 is true and statement-2 is correct explanation for statement -1.
B) Statement -1 is true, statement -2 is true and Statement-2 is NOT correct explanation for statement -1.
C) Statement-1 is true, Statement-2 is false
D) Statement-1 is false, statement -2 is true
Correct Answer: A
Solution :
On squaring we get \[x+1+x-1-2\sqrt{{{x}^{2}}-1}=4x-1\] \[-2\sqrt{{{x}^{2}}-1}=2x-1\] On again squaring we get \[4{{x}^{2}}-4=4{{x}^{2}}-4x+1\]\[\Rightarrow \]\[4x=5\]\[\Rightarrow \]\[x=\frac{5}{4}\] as if \[x=\frac{5}{4}\]- then second square root in given equation become imaginary, so no root is there.
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