The equation `(x+3-4(x-1)^(1//2))^(1//2)+(x+8-6(x-1)^(1//2))^(1//2)=1` has (A) no solution (B) only `1` solution (C) only `2` solutions (D) more than `2` solutions

Options

A. no solution
B. only `1` solution
C. only `2` solutions
D. more than `2` solutions

Answer

D

Explanation

`(d)` Put `(x-1)^(1//2)=t`
or `x=t^(2)+1`
Therefore, the given equation becomes
`(t^(2)+4-4t)^(1//2)+(t^(2)+9-6t)^(1//2)=1`
`implies [(t-2)^(2)]^(1//2)+[(t-3)^(2)]^(1//2)=1`
`implies|t-2|+|t-3|=1`
This equation is satisfied for all values of `t` lying between `2` and `3` i.e.,
`2 le t le 3`
Thus, the given equation is satisfied for all values of `x` lying between `5` and `10`.