Let S=x∈R :x≥0 & 2√x-3+√x √x-6+6=0 . Then S:

Correct answer: (D) Contains exactly two elements. 2√x-3+√x√x-6+6=0 Let √x=t>0 2t-3+tt-6+6=0 ⇒2t-3=-t^2-6t+6 ⇒2t-3=-t^2-6t+9+3 So the equation 2 solutions.

Q59 / 90 · JEE Main 2018 (08 Apr) · Mathematics

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

A
Contains exactly four elements
B
Is an empty set
C
Contains exactly one element
Correct answer
D
Contains exactly two elements

Solution

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

Let $\sqrt{x} = t > 0$

$2 |t - 3| + t (t - 6) + 6 = 0$

$\Rightarrow 2 |t - 3|$ $= - (t^{2} - 6 t + 6)$

$\Rightarrow 2 |t - 3| = - (t^{2} - 6 t + 9) + 3$

So the equation $2$ solutions.

Hence, the correct answer is option: 'D'.

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Let S=x∈R :x≥0 & 2x-3+x x-6+6=0 . Then S:

Solution

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