Question

1. Qual o menor número inteiro que satisfaz a inequação (2x−2)∙(3x−1)≥ (1−3x)²

Answer 1

$\mathrm{(2x-2).(3x-1)\geq (1-3x)^2}\\ \mathrm{6x^2-2x-6x+2\geq1-6x+9x^2}\\ \mathrm{6x^2-8x+2\geq9x^2-6x+1}\\ \mathrm{6x^2-8x+2-9x^2+6x-1\geq0}\\ \mathrm{-3x^2-2x+1\geq0\ \to\ a=-3\ \ \| \ \ b=-2\ \ \| \ \ c=1}\\\\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\ \to\ x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4.(-3).1}}{2.(-3)}}\\\\\\ \mathrm{x=\dfrac{2\pm\sqrt{16}}{-6}\ \to\ x=\dfrac{2\pm4}{-6}\ \to\ x=\dfrac{1\pm2}{-3}}$

$\mathrm{x'=\dfrac{1+2}{-3}\ \to\ x'=-1\ \ \bigg\| \ \ x''=\dfrac{1-2}{-3}\ \to\ x''=\dfrac{1}{3}}\\\\\\ \mathbf{S=\bigg\{x\in\mathbb{R}\ |\ -1\leq x\leq\dfrac{1}{3}\bigg\}\ \to\ \mathrm{Resposta:}\ -1}$