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Solution of \log _{2}\left(x^{2}-5 x+6\right) \geqslant 1 \text { is }

Option: 1

\left ( \infty ,1 \right )


Option: 2

(-\infty, 1] \cup[4, \infty)


Option: 3

\left ( 4,\infty \right )


Option: 4

\Phi


Answers (1)

best_answer

\begin{aligned} & \log _{2}\left(x^{2}-5 x+6\right) \geqslant 1 \\ \Rightarrow & x^{2}-5 x+6 \geqslant 2^{1} \\ \Rightarrow & x^{2}-5 x+4 \geqslant 0 \\ \Rightarrow &(x-1)(x-4) \geqslant 0 \end{aligned}

 

\Rightarrow x \in(-\infty, 1] \cup[4, \infty)

Domain

\begin{aligned} & x^{2}-5 x+6>0 \\ \Rightarrow &(x-2)(x-3)>0 \end{aligned}

\Rightarrow x \in(-\infty, 2) \cup(3, \infty)

Intersection

 

So,x \in(-\infty, 1] \cup[4, \infty)

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mansi

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