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

Options

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

Answer

D

Explanation

The given is meaningful for ` ge1`.
Now,
`sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1`
`implies sqrt((x-1)+4-4sqrt(x-1))+sqrt((x-1)+9-6sqrt(x-1))=1`
`implies |sqrt(x-1)-2|+|sqrt(x-1)-3|=1 " "[:' sqrt(x^(2))=|x|]`
`implies |t-2|+|t-3|=1`, where `x-1=t^(2)`.
This equation is satisfied for all values of t typing between 2 and 3. Thus, the given equation is satisfied for all values of x lying between 5 and 10.