JEE Main On 08 April 2018 Question 7
Question: Let S={$x\in R:x\ge 0 $ and $ |\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0$} . Then S: [JEE Main Online 08-04-2018]
Options:
A) contains exactly two elements.
B) contains exactly four elements.
C) is an empty set.
D) contains exactly one element.
Show Answer
Answer:
Correct Answer: A
Solution:
$ 2| \sqrt{x}-3 |+{{( \sqrt{x} )}^{2}}-6\sqrt{x}+6=0 $
$ 2| \sqrt{x}-3 |+{{( \sqrt{x}-3 )}^{2}}-3=0 $
$ Let| \sqrt{x}-3 |=t $
$ \therefore t^{2}+2t-3=0 $ $ t=1 $ or $ -3 $ (Not possible)
$ \therefore \sqrt{x}=2,4 $
$ \therefore x=4or16 $
