Question

Розв’яжіть систему рівнянь х+у=2 2х²-ху=65

Answer 1

$\left \{ {{x+y=2} \atop {2x^{2}-xy=65 }} \right. x=2-y 2(2-y)^{2} -(2-y)y=65 2(4-4y+y^{2})-2y+y^{2}=65 8-8y+2y^{2}-2y+y^{2} -65=0 3y^{2} -10y-57=0$
$D=100+684=784=28 x_{1}, x_{2} = \frac{10+-28}{6} x_{1} = \frac{10+28}{6}= 6\frac{2}{6} =6 \frac{1}{3} x_{2} = \frac{10-28}{6}= -3$

$6 \frac{1}{3} = 2-y$

$y_{1} =2- 6\frac{1}{3}$

$y_{1} =-4 \frac{1}{3}$

$-3=2-y y_{2}=2+3 y_{2} = 5$

ответ: $(6 \frac{1}{3} ; -4\frac{1}{3}) ; (-3; 5)$