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РИФМИимператрица
@РИФМИимператрица
July 2022
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Решить систему уравнений
1/x-1/y=1/6
xy=6
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sedinalana
Xy=6
1/x-1/y=1/6⇒y-x=xy/6⇒y-x=1⇒y=1+x
x(1+x)=6
x²+x-6=0
x1+x2=-1 U x1*x2=-6
x1=-3⇒y1=-3+1=-2
x2=2⇒y2=2+1=3
(-3;-2);(2;3)
3 votes
Thanks 4
zahargm808
1/x-1/y=1/6
xy=6
6y-6x=xy
x=6/y
6y-6(6/y)=y(6/y)
6y-36/y=6y/y
6y²-36-6y=0
6y²-36=6y
y²-y-6=0
y=-2;3
-2x=6; 3x=6
x=-3; 2
Ответ: x=-3; y=-2 и x=2; y=-3
2 votes
Thanks 2
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Answers & Comments
1/x-1/y=1/6⇒y-x=xy/6⇒y-x=1⇒y=1+x
x(1+x)=6
x²+x-6=0
x1+x2=-1 U x1*x2=-6
x1=-3⇒y1=-3+1=-2
x2=2⇒y2=2+1=3
(-3;-2);(2;3)
xy=6
6y-6x=xy
x=6/y
6y-6(6/y)=y(6/y)
6y-36/y=6y/y
6y²-36-6y=0
6y²-36=6y
y²-y-6=0
y=-2;3
-2x=6; 3x=6
x=-3; 2
Ответ: x=-3; y=-2 и x=2; y=-3