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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

contains exactly four elements

B

is an empty set

C

contains exactly one element

D

contains exactly two elements

Text Solution

Verified by Experts

The correct Answer is:
4
Given equation is `2 |sqrt(x) - 3|+ x - 6 sqrt(x)+6= 0 `
or ` 2 |sqrt(x) - 3|+ (sqrt(x) - 3)^(2) - 3 = 0 `
Let `|sqrt(x) - 3| = y`
` therefore y^(2) + 2y - 3 = 0 `
`rArr (y - 1) (y + 3) = 0 `
` rArr y = 1, - 3 `
`therefore |sqrt(x) - 3| =1`
`rArr sqrt(x) - 3 = pm 1`
`rArr sqrt(x) = 2, 4`
`rArr x = 4, 16 `
So, equation has two solutions.
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