Question

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

Answer 1

Correct Answer - 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`