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leleshka
@leleshka
June 2022
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Решите систему уравнений:[tex] \left \{ {{xy(x+y)=6}, \atop {xy+x+y=5}.} \right. [/tex]
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mukus13
Verified answer
Введем замену
xy=a
x+y=b
a*b=6
a+b=5
a=5-b
(5-b)*b=6
a=5-b
-b²+5b-6=0
решим 2 уравнение
D=25-24=1
b1=3 a1=2
b2=2 a2=3
вернемся к замене
xy=2 или xy=3
x+y=3 x+y=2
x=3-y или x=2-y
y(3-y)=2 y(2-y)=3
x=3-y x=2-y
y²-3y+2=0 или y²-2y+3=0
D=9-8=1 D=4-12<0
y1=2 x1=1 корней нет
y2=1 x2=2
Ответ: (1;2) (2;1)
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Answers & Comments
Verified answer
Введем заменуxy=a
x+y=b
a*b=6
a+b=5
a=5-b
(5-b)*b=6
a=5-b
-b²+5b-6=0
решим 2 уравнение
D=25-24=1
b1=3 a1=2
b2=2 a2=3
вернемся к замене
xy=2 или xy=3
x+y=3 x+y=2
x=3-y или x=2-y
y(3-y)=2 y(2-y)=3
x=3-y x=2-y
y²-3y+2=0 или y²-2y+3=0
D=9-8=1 D=4-12<0
y1=2 x1=1 корней нет
y2=1 x2=2
Ответ: (1;2) (2;1)