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

Answer

2

Explanation

We have `sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5)`
`implies|x|-|x-1|+|x=2|=sqrt(5)`
Case I If `xlt0` then
`-x+(x-1)-(x-2)=sqrt(5)`
`x=1-sqrt(5)`
Case II I `0lexlt1` then
`x+(x-1)-(x-2)=sqrt(5)`
`impliesx=sqrt(5)-1` which is not possible.
Case III If `1lexlt2`, then
`x-(x-1)-(x-2)=sqrt(5)`
`impliesx=3-sqrt(5)` which is not possible.
Case IV If `xgt2`, then
`x-(x-1)+(x-2)=sqrt(5)` ltbr `impliesx=1+sqrt(5)`
Hence number of solutiions is 2.