Question

Exercício 1-Resolva as equações a seguir:
a) 4(x + 2) = -8x + 4
c) x² + 3x +2=0
b) (x + 4) = 5(x + 2)
d) 2x² + 5x-3=0​

Answer 1

Resposta:

$a)\\ \\ 4(x+2)=-8x+4\\ \\ 4x+8=-8x+4\\ \\ 4x-8x=4-8\\ \\ -4x=-4\\ \\ x=\frac{-4}{-4} \\ \\ x=1$

$c)\\ \\ x^{2} +3x+2=0\\ \\ coeficientes:\\ a=1\\ b=3\\ c=2\\ \\ delta=b^{2} -4.a.c\\ \\ delta=3^{2} -4.1.2\\ \\ delta=9-8\\ \\ delta=1\\ \\ x=\frac{-b+-\sqrt{delta} }{2.a} \\ \\ x=\frac{-3+-\sqrt{1} }{2.1} \\ \\ x=\frac{-3+-1}{2} \\ \\ x'=\frac{-3+1}{2} =\frac{-2}{2} =-1\\ \\ x''=\frac{-3-1}{2} =\frac{-4}{2} =-2\\ \\ S\left \{ {{-1;-2} {}} \}$

$b)\\ \\ (x+4)=5(x+2)\\ \\ x+4=5x+10\\ \\ x-5x=10-4\\ \\ -4x=6~~.(-1)\\ \\ 4x=-6\\ \\ x=-\frac{6}{4} \\ \\ x=-\frac{3}{2}$

$d)\\ \\ 2x^{2} +5x-3=0\\ \\ coeficientes:\\ a=2\\ b=5\\ c=-3\\ \\ delta=b^{2} -4.a.c\\ \\ delta=5^{2} -4.2.(-3)\\ \\ delta=25-(-24)\\ \\ delta=25+24\\ \\ delta=49\\ \\ x=\frac{-b+-\sqrt{delta} }{2.a} \\ \\ x=\frac{-5+-\sqrt{49} }{2.2} \\ \\ x=\frac{-5+-7}{4} \\ \\ x'=\frac{-5+7}{4} =\frac{2}{4} =\frac{1}{2} \\ \\ x''=\frac{-5-7}{4} =\frac{-12}{4} =-3\\ \\ S\left \{ {{\frac{1}{2};-3 } {}} \}$