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 $