Number of real roots of the equation `sqrt(x)+sqrt(x-sqrt((1-x)))=1` is

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

We have `sqrt(dx)+sqrt(x-sqrt((-x)))=1`
`impliessqrt(x-sqrt(1-x))=1-sqrt(x)`
On squaring both sides we get
`x-sqrt(1-x)=1+x-2sqrt(x)`
`implies-sqrt(1-x)=1-2sqrt(x)`
Again, squaring on both sides we get
`1-x=1+4x-4sqrt(x)`
`4sqrt(x)=5x`
`impliessqrt(x)=4/5` [on squaring both sides]
`impliesx=16/25`
Hence the number of real solutions is 1.