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Valeryano4ka
@Valeryano4ka
August 2022
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Решить систему уравнений:
x+y+xy=11
xy*(x+y)=30
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Enadoly
X+y=t
xy=m
m+t=11
mt=30
m=11-t
t(11-t)=30
11t-t^2=30
t^2-11t-30=0
D=121-120=1
t1=(11-1)/2=5
t2=6
x+y=6
x+y=5
x=6-y
x=5-y
m=11-6=5
m=11-5=6
xy=5
xy=6
x+y=6
x+y=5
x=5-y
y(5-y)=6
5y-y^2=6
y^2-5y+6=0
D=25-24=1
y=(5-1)/2=2
y=6/2=3
x=3
x=2
ответ (2;3);(3;2);(1;5);(5;1)
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Answers & Comments
xy=m
m+t=11
mt=30
m=11-t
t(11-t)=30
11t-t^2=30
t^2-11t-30=0
D=121-120=1
t1=(11-1)/2=5
t2=6
x+y=6
x+y=5
x=6-y
x=5-y
m=11-6=5
m=11-5=6
xy=5
xy=6
x+y=6
x+y=5
x=5-y
y(5-y)=6
5y-y^2=6
y^2-5y+6=0
D=25-24=1
y=(5-1)/2=2
y=6/2=3
x=3
x=2
ответ (2;3);(3;2);(1;5);(5;1)