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x*y + x*z = 8 y*z + x*y = 18 x*z + y*z = 20
Podstawienie: x*y = a , y*z = b x*z = c
a + c = 8
a + b = 18
b + c = 20
Stronami dodaję
2*a + 2*b + 2*c = 46 |:2
a + b + c = 23
Wykorzystując wcześniejsze dane
b + 8 = 23 ⇒ b = 15
c + 18 = 23 ⇒ c = 5
a + 20 = 23 ⇒ a = 3
Wracam do podstawienia
x*y = 3
y*z = 15
x*z = 5
Stronami mnożę
x2*y2*z2 = 15*5*3 = 152
x*y*z = 15
3*z = 15 ⇒ z = 5 x*15 = 15 ⇒ x = 1 y*5 = 15 ⇒ y = 3
Odp. x = 1 , y = 3 , z = 5
x(y+z)=8
y(z+x)=18
z(x+y)=20
x=8/(y+z)
y(z+ 8/(y+z) )=18
z(8/(y+z) +y) =20
x=8/(y+z)
yz+ 8y/(y+z) =18
8z/(y+z) +yz =20
x=8/(y+z)
yz =18 - 8y/(y+z)
8z/(y+z) +18 - 8y/(y+z) =20
x=8/(y+z)
yz =18 - 8y/(y+z)
8z/(y+z) - 8y/(y+z) =2 /*(y+z)
x=8/(y+z)
yz =18 - 8y/(y+z)
8z - 8y =2*(y+z)
x=8/(y+z)
yz =18 - 8y/(y+z)
8z - 8y =2y+2z →→→6z=10y→→→z=5/3 y
x=8/(y+5/3 y)
y*5/3 y =18 - 8y/(y+5/3 y)
z=5/3 y
x=8/(8/3 y)
5/3 y² =18 - 8y/(8/3 y)
z=5/3 y
x=8* 3/8y
5/3 y² =18 - 8y*3/8y
z=5/3 y
x=3/y
5/3 y² =18 - 3
z=5/3 y
x=3/y
5/3 y² =15 /:5/3
z=5/3 y
x=3/y
y² =9
z=5/3y
x=3/y
y =3 lub y=-3
z=5/3 y
y =3 lub y=-3
x=1 lub x=-1
z=5 lub z=-5
czyli mamy 2 trójki spełniające układ:
91,3,5) oraz (-1,-3,-5)