A) 12
B) 8
C) 4
D) 16
Correct Answer: D
Solution :
| \[|\sqrt{x}-2|+x-4\sqrt{x}=2\]\[\Rightarrow \] \[|\sqrt{x}-2|+{{\left( \sqrt{x} \right)}^{2}}-4\sqrt{x}+4=6\]\[\Rightarrow \] \[{{\left( \sqrt{x}-2 \right)}^{2}}+|\sqrt{x}-2|=6\] |
| Let \[|\sqrt{x}-2|=t\]\[\Rightarrow \] \[{{t}^{2}}+t-6=0\]\[\Rightarrow \] \[(t+3)(t-2)=0\]\[\Rightarrow \]\[t=2\]or \[t=-3\] |
| but \[t=-3\] not possible, |
| \[|\sqrt{x}-2|=2\]\[\Rightarrow \] \[\sqrt{x}-2=\pm 2\]\[\Rightarrow \] \[\sqrt{x}=0\]or\[\sqrt{x}=4\]\[\Rightarrow \]\[x=0\]or\[x=16.\] |
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