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serjonik
@serjonik
July 2022
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Решить систему уравнений
x-y=2
1/x-1/y=-2/3
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zarembo73
x-y=2,
(1)
1/x-1/y=-2/3;
(2)
(1)
x=2+y,
(2)
1/(2+y)-1/y=-2/3;
(y-(2+y))/y(2+y)=-2/3;
2/(y(2+y)=2/3;
Применим основное свойство пропорции:
2y(2+y)=6;
2y
²+4y-6=0; | :2
y²+2y-3=0;
D=4+12=16;
y1=(-2-4)/2=-6/2=-3;
y2=(-2+4)/2=2/2=1;
(1)
x1=2-3=-1;
x2=2+1=3.
Получаем пары чисел:
(-1; -3), (3; 1).
Ответ: (-1; -3), (3; 1).
1 votes
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Answers & Comments
1/x-1/y=-2/3; (2)
(1) x=2+y,
(2) 1/(2+y)-1/y=-2/3;
(y-(2+y))/y(2+y)=-2/3;
2/(y(2+y)=2/3;
Применим основное свойство пропорции:
2y(2+y)=6;
2y²+4y-6=0; | :2
y²+2y-3=0;
D=4+12=16;
y1=(-2-4)/2=-6/2=-3;
y2=(-2+4)/2=2/2=1;
(1) x1=2-3=-1;
x2=2+1=3.
Получаем пары чисел:
(-1; -3), (3; 1).
Ответ: (-1; -3), (3; 1).