The solution set of x2-7 x-10-14 x-x2-45- 0 is

The correct option is C [2,5)∪(5,9)Given nbsp;x^2 7x+1014x x^2 45≥0 ⇒x^2 7x+10x^2 14x+45≤0 ⇒(x 2)(x 5)(x 5)(x 9)≤0 ⇒x 2x 9≤0 [∵ x≠5] From wavy curve metho ...

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Standard XI

Mathematics

Combination of r Things from n Things When All Are Not Different

The solution ...

Question

The solution set of $\frac{x^{2} - 7 x + 10}{14 x - x^{2} - 45} \geq 0$ is

[2, 9]

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[2, 9)

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[2, 5) \cup (5, 9)

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[2, 5) \cup (5, 9]

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Solution

The correct option is C $[2, 5) \cup (5, 9)$
Given $\frac{x^{2} - 7 x + 10}{14 x - x^{2} - 45} \geq 0$
$\Rightarrow \frac{x^{2} - 7 x + 10}{x^{2} - 14 x + 45} \leq 0 \Rightarrow \frac{(x - 2) (x - 5)}{(x - 5) (x - 9)} \leq 0 \Rightarrow \frac{x - 2}{x - 9} \leq 0 [∵ x \neq 5]$

From wavy curve method,
$x \in [2, 9) - {5}$

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The solution set of x2−7x+1014x−x2−45≥0 is

The correct option is C [2,5)∪(5,9)Given x2−7x+1014x−x2−45≥0 ⇒x2−7x+10x2−14x+45≤0⇒(x−2)(x−5)(x−5)(x−9)≤0⇒x−2x−9≤0 [∵x≠5] From wavy curve method, x∈[2,9)−{5}

The solution set of $\frac{x^{2} - 7 x + 10}{14 x - x^{2} - 45} \geq 0$ is