Решите систему уравнений

Question 1

Question 2

какую из них?

Question 3

все

Question 4

$1) \ \left \{ {{x+y=4} \atop {xy=4}} \right. \ \ \left \{ {{y=4-x} \atop {xy=4}} \right. \\ \\ x(4-x) = 4 \ ; \\ \\ - x^{2} + 4x - 4 = 0 \\ \\ x_{1,2} = 2 \\ \\ y_{1,2} = 4-2 = 2$

Ответ: х = 2; у = 2

$2) \ \left \{ {{a+b=2} \atop {ab=-48}} \right. \ \ \left \{ {{b=2-a} \atop {ab=-48}} \right. \\ \\ a(2-a) = -48 \ ; \\ \\ - a^{2} + 2a +48 = 0 \\ \\ a_{1} = -6 \ ; \ a_{2} = 8 \\ \\ b_{1} = 2-(-6) = 8 \ ; \ b_{2} = 2-8 = -6$

Ответ:
$a_{1} = -6 \ ; \ b_{1} = 8 \\ \\ a_{2} = 8 \ ; \ b_{2} = -6$

$3) \ \left \{ {{x+y=3} \atop {xy=-10}} \right. \ \ \left \{ {{y=3-x} \atop {xy=-10}} \right. \\ \\ x(3-x) = -10 \ ; \\ \\ - x^{2} + 3x +10 = 0 \\ \\ x_{1} = -2 \ ; \ x_{2} = 5 \\ \\ y_{1} = 3-(-2) = 5 \ ; \ y_{2} = 3-5 = -2$

Ответ:
$x_{1} = -2 \ ; \ y_{1} = 5 \\ \\ x_{2} = 5 \ ; \ y_{2} = -2$

$4) \ \left \{ {{y+z=-5} \atop {yz=6}} \right. \ \ \left \{ {{z=-5-y} \atop {yz=6}} \right. \\ \\ y(-5-y) = 6 \ ; \\ \\ - y^{2} - 5y - 6 = 0 \\ \\ y_{1} = -3 \ ; \ y_{2} = -2 \\ \\ z_{1} = - 5 - (-3) = - 2 \ ; \ z_{2} = - 5 - (-2) = - 3$

Ответ:
$y_{1} = -3 \ ; \ z_{1} = -2 \\ \\ y_{2} = -2 \ ; \ z_{2} = -3$

$5) \ \left \{ {{m+n=-3} \atop {mn=-18}} \right. \ \ \left \{ {{m=-3-n} \atop {mn=-18}} \right. \\ \\ n(-3-n) = -18 \ ; \\ \\ - n^{2} - 3n + 18 = 0 \\ \\ n_{1} = -6 \ ; \ n_{2} = 3 \\ \\ m_{1} = - 3 - (-6) = 3 \ ; \ m_{2} = - 3 - 3 = - 6$

Ответ:
$n_{1} = -6 \ ; \ m_{1} = 3 \\ \\ n_{2} = 3 \ ; \ m_{2} = -6$

$6) \ \left \{ {{u+v=15} \atop {uv= 56}} \right. \ \ \left \{ {{v=15-u} \atop {uv=56}} \right. \\ \\ u(15-u) = 56 \ ; \\ \\ - u^{2} +15u -56 = 0 \\ \\ u_{1} = 7 \ ; \ u_{2} = 8 \\ \\ v_{1} = 15 - 7 = 8 \ ; \ v_{2} = 15 - 8 = 7$

Ответ:
$u_{1} = 7 \ ; \ v_{1} = 8 \\ \\ u_{2} = 8 \ ; \ v_{2} = 7$