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Vikitori666
@Vikitori666
August 2021
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помогите пожалуйста с 588!!! ну пожалуйста!
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anna1420
1) х - y = 7
xy = 18
______________
x = 7 + y
подставляем во второе уравнение вместо х
получается
(7 + y) * y = 18
y^2 + 7y - 18 = 0
D = 49 + 4*18 = 121= 11^2
y1 = (-7 + 11)/2 = 2
y2 = (-7 - 11)/2 = -9
значит корни х1 = 9
х2 = -2
2) x - y = 2
xy = 15
_______________
x = 2 + y
y^2 + 2y - 15 = 0
D = 64
y1 = 3 x1 = 5
y2 = -5 x2 = -3
3) х + у = 2
ху = -15
_______________
х = 2 - у
подставляем во второе
( 2 - у )*у = -15
у^2 - 2y - 15 = 0
D = 64
y1 = 5 x1 = -3
y2 = -3 x2 = 5
4) x + y = -5
xy = -36
______________
x = - 5 - y
y^2 + 5y -36 = 0
D = 169
y1 = 4 x1 = -9
y2 = -9 x2 = 4
5) x^2 + y^2 = 13
xy = 6
__________________
x = 6/y
подставляем в первое
36/y^2 + y^2 = 13
y^4 - 13y^2 + 36 = 0
назначим y^2 = t
t^2 - 13t + 36 = 0
D = 25
t1 = 4
t2 = 9
y^2 = 9
y^2
= 4
y1 = +/- 3
y2 = +/-2
x2 = +/-2
x1= +/- 3
6) x^2 + y^2 = 41
xy = 20
____________________
x = 20/y
400/y^2 + y^2 = 41
y^4 - 41y^2 + 400 = 0
t^2 - 41 t + 400 = 0
D = 81
t1 = 16
t2 = 25
y^2 = 16
y^2 = 25
y1 = +/- 4
y2 = +/- 5
x1 = +/- 5
y2 = +/- 4
1 votes
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Answers & Comments
xy = 18
______________
x = 7 + y
подставляем во второе уравнение вместо х
получается
(7 + y) * y = 18
y^2 + 7y - 18 = 0
D = 49 + 4*18 = 121= 11^2
y1 = (-7 + 11)/2 = 2
y2 = (-7 - 11)/2 = -9
значит корни х1 = 9
х2 = -2
2) x - y = 2
xy = 15
_______________
x = 2 + y
y^2 + 2y - 15 = 0
D = 64
y1 = 3 x1 = 5
y2 = -5 x2 = -3
3) х + у = 2
ху = -15
_______________
х = 2 - у
подставляем во второе
( 2 - у )*у = -15
у^2 - 2y - 15 = 0
D = 64
y1 = 5 x1 = -3
y2 = -3 x2 = 5
4) x + y = -5
xy = -36
______________
x = - 5 - y
y^2 + 5y -36 = 0
D = 169
y1 = 4 x1 = -9
y2 = -9 x2 = 4
5) x^2 + y^2 = 13
xy = 6
__________________
x = 6/y
подставляем в первое
36/y^2 + y^2 = 13
y^4 - 13y^2 + 36 = 0
назначим y^2 = t
t^2 - 13t + 36 = 0
D = 25
t1 = 4
t2 = 9
y^2 = 9
y^2 = 4
y1 = +/- 3
y2 = +/-2
x2 = +/-2
x1= +/- 3
6) x^2 + y^2 = 41
xy = 20
____________________
x = 20/y
400/y^2 + y^2 = 41
y^4 - 41y^2 + 400 = 0
t^2 - 41 t + 400 = 0
D = 81
t1 = 16
t2 = 25
y^2 = 16
y^2 = 25
y1 = +/- 4
y2 = +/- 5
x1 = +/- 5
y2 = +/- 4