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VirusX · Answer 1 · 2023-09-21T23:33:29+0000

Solution:

Given:

Factorizing the function;

$\begin{gathered} x^2-4x+3=x^2-3x-x+3 \\ =x(x-3)-1(x-3) \\ =(x-1)(x-3) \end{gathered}$

Hence,

$\begin{gathered} x^2-4x+3\leq0 \\ (x-1)(x-3)\leq0 \end{gathered}$

To get the solution, it must satisfy the condition of the inequality given.

$ab\leq0,\text{ }a\ge0,b\leq0$

Hence,

$\begin{gathered} (x-1)(x-3)\leq0 \\ x-1\ge0,x-3\leq0 \\ x\ge1,x\leq3 \\ \\ Combining\text{ the two inequalities, the solution is;} \\ 1\leq x\leq3 \end{gathered}$

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