The number of integers in solution set of -x-3 -2-x-2 is

Given nbsp;√(x) 3 ≤2√(x) 2 will be valid if x≥0,x≠4 Let √(x)=t, t≥0 t 3 ≤2t 2 ⇒ (t 3) 2t 2≤ 0 (t 3)(t 2) 2t 2≤ 0 t^2 5t+4t 2≤ 0 (t 1)(t 4)t 2≤ 0, (t≠2) ⇒ ...

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Standard XII

Mathematics

Inequality

The number of...

Question

The number of integers in solution set of $\sqrt{x} - 3 \leq \frac{2}{\sqrt{x} - 2}$ is

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Solution

Given $\sqrt{x} - 3 \leq \frac{2}{\sqrt{x} - 2}$ will be valid
if $x \geq 0, x \neq 4$

Let $\sqrt{x} = t, t \geq 0$
$t - 3 \leq \frac{2}{t - 2}$
$\Rightarrow (t - 3) - \frac{2}{t - 2} \leq 0$
$\frac{(t - 3) (t - 2) - 2}{t - 2} \leq 0$
$\frac{t^{2} - 5 t + 4}{t - 2} \leq 0$
$\frac{(t - 1) (t - 4)}{t - 2} \leq 0, (t \neq 2)$
$\Rightarrow t \in [0, 1] \cup (2, 4] ∴ x \in [0, 1] \cup (4, 16]$

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The number of integers in solution set of √x−3≤2√x−2 is

Given √x−3≤2√x−2 will be valid if x≥0,x≠4 Let √x=t, t≥0 t−3≤2t−2 ⇒(t−3)−2t−2≤0 (t−3)(t−2)−2t−2≤0 t2−5t+4t−2≤0 (t−1)(t−4)t−2≤0, (t≠2) ⇒t∈[0,1]∪(2,4]∴x∈[0,1]∪(4,16]

The number of integers in solution set of $\sqrt{x} - 3 \leq \frac{2}{\sqrt{x} - 2}$ is