Question

A solução que pertence a inequação x² - 4x + 3 < 0

Answer 1

$\displaystyle x^2-4x+3\ \textless \ 0\\i)~~~~x^2-4x+3\implies X=\frac{4\pm\sqrt{4}}{2}= \left \{ {{x'=\frac{4-2}{2}=2-1=1} \atop {x''=\frac{4+2}{2}=2+1=3}} \right. \\\\ii)~~~(x-3)(x-1)=x^2-4x+3\\\\iii)~~x-3=0\to x=3\\~~~~~~~x-3\ \textgreater \ 0\to x\ \textless \ 3\\~~~~~~~x-3\ \textless \ 0\to x\ \textgreater \ 3\\\\iv)~~x-1=0\to x=1\\~~~~~~~x-1\ \textgreater \ 0\to x\ \textless \ 1\\~~~~~~~x-1\ \textless \ 0\to x\ \textgreater \ 1$
Verificando chega-se:
$1\ \textless \ x\ \textless \ 3$