Question

Resolva a inequação x . (x – 1) (-x + 2) ≤ 0

a) {x R / 0 ≤ x ≤ 1 }

b) {x R / ou x ≥ 2}

c) {x R / x=0}

d) {x R / 0 ≤ x ≤ 1 ou x ≥ 2}

e) {x R / 0 ≤ x ≤ 2 ou x ≥ 2}​

Answer 1

$\boxed{\begin{array}{l}\sf interprete~cada~parcela\\\sf do~produto~como~func_{\!\!,}\tilde ao:\\\sf f(x)=x~~g(x)=x+1~~h(x)=-x+2\\\underline{\rm estudo~do~sinal~de~f(x):}\\\sf f(x)>0~~para~~x>0~e~~f(x)<0~para~~x<0\\\underline{\rm estudo~do~sinal~de~g(x):}\\\sf g(x)>0~~para~~x>1~~e~~g(x)<0~~para~x<1\\\underline{\rm estudo~do~sinal~de~h(x):}\\\sf h(x)>0~~para~~x<2~e~~h(x)<0~~para~~x>2\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm observe~a~figura~que~anexei}\\\\\underline{\rm montando~um~quadro~sinal}\\\underline{\rm e~assinalando~a~resposta~temos:}\\\\\sf S=\{x\in\mathbb{R}/0\leqslant x\leqslant1~~ou~x\geqslant2\}\end{array}}$