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Let S={x in R: x ge 0 and 2|(sqrt(x)-3|+...

Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S (1) is an empty set (2) contains exactly one element (3) contains exact;y two elements (4) contains exactly four elements

A

is an empty set

B

xcontains exactly one element

C

contains exactly two elements

D

contains exactly four elements

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `2|sqrtx-3|+sqrtx(sqrtx-6)+6=0`
Let `sqrtx-3=y`
`impliessqrtx=y+3`
`therefore2|y|+(y+3)(y-3)+6=0`
`implies2|y|+y^(2)-3=0`
`implies|y|^(2)+2|y|-3=0`
`(|y|+3)(|y-1)=0`
`implies|y|ne-3implies|y|=1`
`impliesy=+-1impliessqrtx-3=+-1`
`impliessqrtx=4,2impliesx=16,4`
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