A) 0
B) 1
C) 2
D) 3
Correct Answer: B
Solution :
[b] \[\sqrt{x}+\sqrt{x-\sqrt{1-x}}=1\] \[\Rightarrow \sqrt{x-\sqrt{1-x}}=1-\sqrt{x}=x-\sqrt{1-x}=1+x-2\sqrt{x}\]\[\Rightarrow -\sqrt{1-x}=1-2\sqrt{x}\Rightarrow 1-x=1+4x-4\sqrt{x}\] \[\Rightarrow 4\sqrt{x}=5x\therefore x=\frac{16}{25}\,\,or\,\,0.\] Now \[x=0\]does not satisfy but \[x=\frac{16}{25}\] satisfies the equation. The only solution is \[x=\frac{16}{25}\]
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