Question

Решите систему уравнений

Answer 1

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

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