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The equation sqrt(x+1) - sqrt(x-1) = sqr...

The equation `sqrt(x+1) - sqrt(x-1) = sqrt(4x-1)` has

A

no solution

B

one solution

C

two solutions

D

more than two solutions

Text Solution

Verified by Experts

The correct Answer is:
A
Since `sqrt(x+1)-sqrt(x-1)=sqrt(4x-1)`
`implies(x+1)+(x-1)-2sqrt(x^(2)-1)=4x-1`
`implies1-2x=2sqrt(x^(2)-1)implies1+4x^(2)-4x=4x^(2)-4`
`implies 4x=5impliesx=5/4`
But it does not satisfy the given equation. Hence, no solution exists.
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