Theory of Equations 1 Question 12

13. Let $S={x \in \mathbf{R}: x \geq 0and2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0.Then,S$

(2018 Main)

(a) is an empty set

(b) contains exactly one element

(c) contains exactly two elements

(d) contains exactly four elements

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Solution:

  1. We have, 2|x3|+x(x6)+6=0

 Let x3=yx=y+32|y|+(y+3)(y3)+6=02|y|+y23=0|y|2+2|y|3=0(|y|+3)(|y|1)=0|y|3|y|=1y=±1x3=±1x=4,2x=16,4



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