Equations And Inequalities Question 36
Question: 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
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ \sqrt{x}+\sqrt{x-\sqrt{1-x}}=1 $
$ \Rightarrow \sqrt{x-\sqrt{1-x}}=1-\sqrt{x}=x-\sqrt{1-x}=1+x-2\sqrt{x} $
$ \Rightarrow -\sqrt{1-x}=1-2\sqrt{x}\Rightarrow 1-x=1+4x-4\sqrt{x} $
$ \Rightarrow 4\sqrt{x}=5x\therefore x=\frac{16}{25}or0. $ Now $ x=0 $ does not satisfy but $ x=\frac{16}{25} $ satisfies the equation. The only solution is $ x=\frac{16}{25} $
BETA
