Вот накалякал. Разбирайся :)
xy/(x+y) = 5
xz/(x+z) = 7
yz/(y+z) = 9
xy = 5x + 5y
xz = 7x + 7z
yz = 9y + 9z
x(y-5) = 5y
x = 5y/(y-5)
5yz/(y-5) = 35y/(y-5) + 7z
5yz = 35y + 7z * (y-5)
5yz = 35y + 7yz - 35z
2yz + 35y = 35z
y(2z + 35) = 35z
y = 35z/(2z + 35) = z/(2z/35 + 1)
35z^2/(2z + 35) = 315z/(2z + 35) + 9z
35z^2 = 315z + 9z*(2z + 35)
35z^2 = 315z + 18z^2 + 315z
17z^2 = 630z
z=630/17
y = 35*630/(2*630/17 + 35)/17 = 35*630/(1260 + 595) = 22050/1855 = 630 / 53
x = 5*630/(630/53 - 5)/53 = 5*630/((630/53 - 5)*53) = 5*630/365 = 630/73
a=1
b=0
c=1
Объяснение:
abc (a+2b):(b+2c):(c+2a)=1:2:3
{a+2b=1 {a=1-2b
{b+2c=2 {b=2-2c
{c+2a=3 {c=3-2a
a=1-2[2-2(3-2a)]
a=1-2(2-6+4a)
a=1-4+12-8a
9a=9 // : 9
a=1
b=2-2((3-2*1)
b=2-6+4
b=0
c=3-2*1
c=3-2
c=1
prowierka:
a+2b=1
1+0=1
1=1
b+2c=2
0+2*1=2
2=2
c+2a=3
1+2*1=3
3=3