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The number of solutions of the equation ...

The number of solutions of the equation
`sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5)` is

A

`0`

B

`1`

C

`2`

D

More than `2`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `|x|-|x-1|+|x-2|=sqrt(5)`
For `x ge 2`,
`x-(x-1)+x-2=sqrt(5)impliesx=1+sqrt(5)`
For ` 1 le x le 2`,
`x-(x-1)+(2-x)=sqrt(5)`
`x=3-sqrt(5)` No solution
For `0 le x lt 1`,
`x-(1-x)+2-x=sqrt(5)`
`x=sqrt(5)-1` No solution
For `x lt 0`,
`-x-(1-x)+2-x=sqrt(5)`
`x=1-sqrt(5)`
Hence, `x=sqrt(5)+1` or `x=1-sqrt(5)`
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