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ferandi
@ferandi
August 2022
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решите систему уравнений
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Verified answer
В первом уравнении можно выделить полный квадрат...
(xy)² - 2*xy*3 + 9 - 4 = 0
(xy - 3)² - 2² = 0
(xy - 3 - 2)(xy - 3 + 2) = 0
xy = 5 или xy = 1
-----------------------------получим две системы)))
1) x = 5/y
3*5/y + 3y = 10
15 + 3y² - 10y = 0
D = 100-4*3*15 = 20*(5-9) < 0 ---нет решений)))
2) x = 1/y
3/y + 3y = 10
3 + 3y² - 10y = 0
D = 100-4*3*3 = 4*(25-9) = (2*4)²
(y)1;2 = (10+-8)/6
y1 = 1/3 x1 = 3
y2 = 3 x2 = 1/3
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Answers & Comments
Verified answer
В первом уравнении можно выделить полный квадрат...(xy)² - 2*xy*3 + 9 - 4 = 0
(xy - 3)² - 2² = 0
(xy - 3 - 2)(xy - 3 + 2) = 0
xy = 5 или xy = 1
-----------------------------получим две системы)))
1) x = 5/y
3*5/y + 3y = 10
15 + 3y² - 10y = 0
D = 100-4*3*15 = 20*(5-9) < 0 ---нет решений)))
2) x = 1/y
3/y + 3y = 10
3 + 3y² - 10y = 0
D = 100-4*3*3 = 4*(25-9) = (2*4)²
(y)1;2 = (10+-8)/6
y1 = 1/3 x1 = 3
y2 = 3 x2 = 1/3