Question

(x-3)^3 -1 / (x-1)^3 > 1

Answer 1

Resposta:

$\frac{15}{12}<x<\frac{33}{12}$

Explicação passo-a-passo:

$\frac{(x-3)^3 -1}{(x-1)^3}>1 \Rightarrow  x^3-9x^2+27x-27-1=(x-1)^3\Rightarrow \\\\x^3-9x^2+27x-28=x^3-3x^2+3x-1\Rightarrow-9x^2+27x-27=-3x^2+3x\Rightarrow\\\\ \Rightarrow 6x^2-24x+27<0 \\\\\\ x=\frac{24\pm\sqrt{729-648}}{12} \\\\ x=\frac{24\pm\sqrt{81}}{12}\\\\ x=\frac{24\pm9}{12}\\\\ x'=\frac{24+9}{12}=\frac{33}{12}\\\\ x''=\frac{24-9}{12} =\frac{15}{12}\\\\ S: \frac{15}{12}<x<\frac{33}{12}$