Question

sistema de equaçoes de 2° grau:
Xy=6
2x-y=1

Answer 1

$\left \{ {{2x-y=1} \atop {xy=2}} \right. \\ \\ isola~~y={6\over x} \\ \\ substituir~~y~~em \\ \\ 2x-y=1 \\ 2x-{6\over x}=1 \\ \\ mmc=x \\ \\ 2x^2-6=x \\ 2x^2-x-6=0 \\ \\ a=2 \\ b=-1 \\ c=-6 \\ \\ \Delta=b^2-4ac \\ \Delta=(-1)^2-4(2)(-6) \\ \Delta=1+48 \\ \Delta=49 \\ \\ x={-b\pm \sqrt{\Delta} \over 2a}={-(-1)\pm \sqrt{49} \over2.(2)}={1\pm7\over4} \\ \\ x'={1+7\over4}={8\over4}=2 \\ \\ x"={1-7\over4}=-{6\over4}=-{3\over2}$


$Se~~y={6\over x} \\ \\ p/~~x'=3 \\ \\ y'={6\over3} \\ y'=2 \\ \\ p/~~x"=-{3\over2} \\ \\ y"=6\div(- \frac{3}{2} ) \\ \\ y"=6\times(-\frac{2}{3}) \\ \\ y"=-\frac{12}{3} \\ \\ y"=-4 \\ \\ S=\{(2,3);(-\frac{3}{2},-4)\}$