Question

{3x-4y=12
{x.y=180
caculo.​

Answer 1

Resposta:

$\begin{cases}</p><p> 3x - 4y =\ 12 \Rightarrow \: 3x = 4y + 12 \Rightarrow \: x = \frac{4y + 12}{3} \\</p><p> xy =\ 180</p><p>\end{cases} \\ xy = 180 \\ ( \frac{4y + 12}{3} ).y = 180 \\ \frac{4 {y}^{2} + 12y}{3} = 180 \\ 4 {y}^{2} + 12y = 180.3 \\ 4 {y}^{2} + 12y = 540 \\ 4 {y}^{2} + 12y - 540 = 0 \\ {y}^{2} + 3y - 135 = 0$

∆ = b² - 4ac

∆ = 3² - 4.1.(-135)

∆ = 9 + 540

∆ = 549

$y = \frac{ - b \pm \sqrt{ \Delta} }{2a} \\ y = \frac{ - 3 \pm \sqrt{549} }{2.1} \\ y = \frac{ - 3 \pm3 \sqrt{61} }{2}$

$x = \frac{4y + 12}{3} \\ x = \frac{4.( \frac{ - 3 \pm3 \sqrt{61} }{2}) }{3} \\ x = \frac{2.( - 3 \pm3 \sqrt{61}) }{3} \\ x = 2.( - 1 \pm \sqrt{61} ) \\ x = - 2 \pm2 \sqrt{61}$