Решите систему управления х+у=5 ху=4

[latex] \left \{ {{x+y=5} \atop {xy=4}} \right. [/latex] [latex] \left \{ {{x=5-y} \atop {xy=4}} \right. [/latex] (5-y)y=4 5y-[latex] y^{2} [/latex] = 4 - [latex] y^{2} [/latex] + 5y - 4 = 0 a =-1  b=5 c=-4 D = [latex] b^{2} [/latex]-4ac D = [latex] 5^{2} [/latex] - 4 * (-1) * (-4) = 25 - 16 = 9  [latex] \sqrt{D} = \sqrt{9} = 3[/latex] [latex] y_{1} = \frac{-b+ \sqrt{D} }{2a} = \frac{-5+3}{-2} = \frac{-2}{-2} = 1[/latex] [latex] y_{2} = \frac{-b- \sqrt{D} }{2a} = \frac{-5-3}{-2} = \frac{-8}{-2} =4[/latex] [latex] \left \{ {{y_{1} =1 ; y_{2}=4 } \atop {x=5-y}} \right. [/latex] [latex] x_{1} = 5 - y_{1} = 5-1=4 [/latex] [latex] x_{2} = 5- y_{2} = 5-4=1[/latex] Ответ. (4;1), (1;4)