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

Options

A. no solution
B. one solution
C. two solutions
D. more than two solutions

Answer

A

Explanation

we have,
`sqrt(x+1)-sqrt(x-1)=sqrt(4x-1)" "`............(i)
`implies(sqrt(x+1)-sqrt(x-1))^(2)=(sqrt(4x-1))^(2)`
`impliesx+1+x-1-2sqrt(x^(2)-1)=4x-1`
`implies 2x-2sqrt(x^(2)-1)=2x-1`
`-2sqrt(x^(2)-1)=2x-1`
`implies 4(x^(2)-1)=(2x-1)^(2)`
`implies 4x^(2)-4-4x^(2)-4x+1 implies x=5//4`
But, `x=(5)/(4)` does not satisfy equation (i).
Hence, equation (i) has no solutions.