SATHEE: Theory of Equations 1 Question 12

Theory of Equations 1 Question 12

13. Let $S = x \in R : x \geq 0$ and $2 | \sqrt{x} - 3 | + \sqrt{x} (\sqrt{x} - 6) + 6 = 0$ . Then, $S$

(2018 Main)

(a) is an empty set

(b) contains exactly one element

(d) contains exactly four elements

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Answer:

Correct Answer: 13. (c)

Solution:

We have, $2 | \sqrt{x} - 3 | + \sqrt{x} (\sqrt{x} - 6) + 6 = 0$

$\begin{aligned} Let \sqrt{x} - 3 = y \\ \Rightarrow \sqrt{x} = y + 3 \\ ∴ 2 | y | + (y + 3) (y - 3) + 6 = 0 \\ \Rightarrow 2 | y | + y^{2} - 3 = 0 \\ \Rightarrow | y |^{2} + 2 | y | - 3 = 0 \\ \Rightarrow (| y | + 3) (| y | - 1) = 0 \\ \Rightarrow | y | \neq - 3 \Rightarrow | y | = 1 \\ \Rightarrow y = \pm 1 \Rightarrow \sqrt{x} - 3 = \pm 1 \\ \Rightarrow \sqrt{x} = 4, 2 \Rightarrow x = 16, 4 \end{aligned}$

Theory of Equations 1 Question 12

13. Let $S = x \in R : x \geq 0$ and $2 | \sqrt{x} - 3 | + \sqrt{x} (\sqrt{x} - 6) + 6 = 0$ . Then, $S$

Answer:

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Theory of Equations 1 Question 12

13. Let S=x∈R:x≥0 and 2|x−3|+x(x−6)+6=0. Then, S

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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13. Let $S = x \in R : x \geq 0$ and $2 | \sqrt{x} - 3 | + \sqrt{x} (\sqrt{x} - 6) + 6 = 0$ . Then, $S$