Question

Resolva as equações a seguir: a) (x+1/2)(x-2/3)=0 b) (x-10)(x+20)=0

Answer 1

$a) \\ (x+ \frac{1}{2} )(x- \frac{2}{3} )=0 \\ \\ x^2- \frac{2}{3} x+ \frac{1}{2} x- \frac{2}{6} =0 \\ \\ 6x^2-6. \frac{2}{3} x+6. \frac{1}{2} x-6. \frac{2}{6} =0 \\ \\ 6x^2-4x+3x-2=0 \\ \\ 6x^2-x-2=0$

Equação de 2º grau resolução pela fórmula de Bhaskara

$delta = 1+4.6.2=49$

$\sqrt{delta} = \sqrt{49} =7 \\ \\ x_{1} = \frac{1+7}{12} = \frac{4}{3} \\ \\ x_{2} = \frac{1-7}{12} =- \frac{6}{12} =- \frac{1}{2}$

S={$- \frac{1}{2} , \frac{4}{3}$}

$b) \\ (x-10)(x+20)=0 \\ \\ x^2+20x-10x-200=0 \\ \\ x^2+10x-200=0 \\ \\ delta=100+4.1.200=900 \\ \\ \sqrt{delta} = \sqrt{900} =30 \\ \\ x_{1} = \frac{-10+30}{2} = \frac{20}{2} =10 \\ \\ x_{2} = \frac{-10-20}{2} =- \frac{40}{2} =-20$

S={-20,10}