5х²-6ху+5у²=29
7х²-8ху+7у²=43
--
5х²-10ху+5у²+4xy=29
7х²-14ху+7у²+6xy=43
--
5(x²-2ху+у²)+4ху=29
7(х²-2ху+у²)+6ху=43
5(x-у)²+4ху=29
7(х-у)²+6ху=43
замена
ху=а
(х-у)²=b
5b+4а=29 |*6
7b+6а=43 |*4
--
5b+4а=29 |*6
7b+6а=43 |*4
--
30b + 24a = 174
28b + 24a = 172
--
вычитаем
2b = 2
b = 1
5*1 + 4a = 29
4a = 24
a = 6
--
ху=6
(х-у)²=1
|x - y| = 1
1. x - y = 1
x = 1 + y
y(y + 1) = 6
y² + y - 6 = 0
D = 1 + 24 = 25
y12=(-1 +- 5)/2 = -3 2
y1 = -3 x1 = -2
y2 = 2 x2 = 3
2. x - y = -1
x = -1 + y
y(y - 1) = 6
y² - y - 6 = 0
D = 1 + 24 = 25
y12=(1 +- 5)/2 = 3 -2
y1 = 3 x1 = 2
y2 = -2 x2 = -3
ответ (-2, -3) (3,2) (2,3) (-3,-2)
