The equation `sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=` hs

Options

A. No solution
B. Exactly two distinct solutions
C. Exactly four distinct solutions
D. Infinitely may solutions

Answer

D

Explanation

`sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1,Xge1`
`sqrt((x+1)-2xx2sqrt(x-1)+4)+sqrt((x-1)-6sqrt(x-1)+9)=1`
`|sqrt(x-1)-2|+|sqrt(x-1)-3|=1`
Case - 1
`sqrt(x-1)-2+sqrt(x-1)-3=1" "xge10`
`2sqrt(x-1)=6`
x = 10
Case - II
`sqrt(x-1)-2-sqrt(x-1)+3=1" "5lexle10`
Case - III
`-sqrt(x-1)+2-sqrt(x-1)+3=1" "1lexle5`
`2sqrt(x-1)=4`
x = 5