решить систему x+y=5 2xy-y^2=-13. Created by vitalik2112. algebra-ru

решить систему x+y=5 2xy-y^2=-13...

Gerren X+y=52xy-y^2=-13из 1-го выразим x=5-y подставим во 2-е
2y(5-y)-y²=-13
10y-2y²-y²=-13
3y²-10y-13=0
D=100+156=256=16²
y₁₂=(10+-16)/6= -1 26/6
y₁=-1 x₁=6
y₂=13/3 x₂=5 - 13/3=(15-13)/3=2/3
ответ (6 -1) (2/3 13/3)

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mmb1

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Из 1-го выразим y=5-x подставим во 2-е
2x(5-x)-(5-x)^2=-13
10x-2x^2-25+10x-x^2+13=0
-3x^2+20x-12=0
3x^2-20x+12=0
D=100-36=64
x1=(10+8)/3=6
x2=(10-8)/3=2/3
y1=5-6=-1
y2=5-2/3=13/3
(6;-1),(2/3;13/3)

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