Question

resolva a equação x-2/3x+2x-1/2=5x+2/6 : a){-1,3} b){-1,4} c){1,-4} d){1,-3}​

Answer 1

Resposta: Alternativa B (-1,4)

Explicação passo-a-passo:

$\frac{x-2}{3x}+\frac{2x-1}{2}=\frac{5x+2}{6}, x\neq    0\\\frac{2(x+2)}{x}+3(2x-1)=5x+2, x\neq  0\\\frac{2(x-2)}{x}+3(2x-1)-5x-2=0\\\frac{2x-4}{x}+6x-3-5x-2=0\\\frac{2x-4}{x}+x-5=0\\ \frac{2x-4+x^2-5x}{0}=0\\\frac{-3x-4+x^2}{x}=0\\-3x-4=x^2=0\\x^2-3x-4=0\\x=\frac{-(-3±\sqrt{(-3)^2-4.1.(-4)}}{2.1}\\ x=\frac{3±\sqrt{9+16}}{2}\\x=\frac{3±\sqrt{25}}{2}\\x=\frac{3±5}{2}\\x=\frac{3+5}{2}=\frac{8}{2}=4\\x=\frac{3-5}{2}=\frac{-2}{2}=-1$

Answer 2

Resposta:

Letra B

Explicação passo-a-passo:

${x-2\over3x}+{2x-1\over2}={5x+2\over6}\\ \\ mmc=6x\\ \\ 2(x-2)+3x(2x-1)=x(5x+2)\\ \\ 2x-4+6x^2-3x=5x^2+2x\\ \\ 6x^2-5x^2+2x-3x-2x-4=0\\ \\ x^2-3x-4=0\\ \\ a=1\\ b=-3\\ c=-4\\ \\ \Delta=b^2-4ac\\ \Delta=(-3)^2-4(1)(-4)\\ \Delta=9+16\\ \Delta=25\\ \\ x={-b\pm\sqrt{\Delta} \over2a}={-(-3)\pm\sqrt{25} \over2}={3\pm5\over2}\\ \\ x'={3+5\over2}={8\over2}=4\\ \\ x"={3-5\over2}=-{2\over2}=-1\\ \\ S=\{-1,4\}$