Question

Resolva o sistema de equação do segundo grau


{X + y = 3 x²+ 2y²= 9


{2x-y= -2 x²+y -2x= 3

Answer 1

a)

$</p><p>\begin{cases} x+y=3\\{x}^{2}+2{y}^{2}=9\end{cases}$

$x+y=3 \\ y=3-x$

${x}^{2}+2{y}^{2}=9 \\{x}^{2}+2{(3-x)}^{2}=9$

${x}^{2}+2(9-6x+{x}^{2})=9 \\ {x}^{2}+18-12x+2{x}^{2}=9$

$3{x}^{2}-12x+18-9=0$

$3{x}^{2}-12x+9=0\div3$

${x}^{2}-4x+3=0$

$\boxed{\Delta={b}^{2}-4ac}$

$\Delta={(-4)}^{2}-4.1.3$

$\Delta=16-12$

$\Delta=4$

$\boxed{x=\frac{-b±\sqrt{\Delta}}{2a}}$

$x=\frac{-(-4)±\sqrt{4}}{2.1}$

$x=\frac{4±2}{2}$

$\boxed{\boxed{x'=\frac{4+2}{2}=\frac{6}{2}=3}}$

$\boxed{\boxed{x''=\frac{4-2}{2}=\frac{2}{2}=1}}$

$\boxed{\boxed{y=3-x=3-3=0}}$

$\boxed{\boxed{y=3-x=3-1=2}}$

s={(3,0),(1,2)}

A outra questão é feita de modo análogo.