Maths六式方程

(a+z)/y=4a......(1)
(b+z)/a=5c......(2)
(c+d)/c=4d......(3)
c/(a*b)=7......(4)
a+y+z=7c......(5)
c+a+y=5z......(6)
(5) - (6) :
z - c = 7c - 5z
z : c = 4 : 3
Let z = 4k , c = 3k , sub to (1) ---- (4) , get (7)----(10) ; sub to (5) or (6) ,
get (11) :
(a + 4k) = 4ay......(7)
(b + 4k) = 15ak......(8)
(3k + d) = 12dk......(9)
3k = 7ab......(10)
a + y = 20k......(11)
By (10) : k = 7ab/3 , sub it to (8) :
(b + 28ab/3) = 35(a^2) b , by (4) b <> 0 , so
(1 + 28a/3) = 35a^2
a = 0.3486220 or - 0.0819553 , sub to (7) and (11) :
When a = 0.3486220 :
0.3486220 + 4k = 1.3944880y
0.3486220 + y = 20k
Solve it : y = 0.3502307 , k = 0.0349426
so z = 4k = 0.1397704 , c = 3k = 0.1048278
By (10) : 0.1048278 = 7(0.3486220)b
b = 0.0429560
By (9) : 0.1048278 + d = 12d(0.0349426)
d = - 0.1805232

When a = - 0.0819553 :
- 0.0819553 + 4k = -0.3278212y
- 0.0819553 + y = 20k
Solve it : y = 0.1863251 , k = 0.0052185
so z = 4k = 0.0208740 , c = 3k = 0.0156555
By (10) : 0.0156555 = 7(- 0.0819553)b
b = - 0.0272893
By (9) : 0.0156555 + d = 12d(0.0052185)
d = - 0.0167014


2010-03-31 21:30:58 補充：
(11) should be

a + y = 17k......(11)

2010-03-31 22:09:50 補充：
a = 0.3486220 or - 0.0819553 , sub to (7) and (11) :

When a = 0.3486220 :

0.3486220 + 4k = 1.3944880y
0.3486220 + y = 17k

Solve it : y = 0.3715088 , k = 0.0423606

so z = 4k = 0.1694424 , c = 3k = 0.1270818

By (10) : 0.1270818 = 7( 0.3486220 )b

b = 0.0520751

By (9) : 0.1270818 + d = 12d(0.0423606)

2010-03-31 22:11:39 補充：
d = - 0.2584682

2010-03-31 22:15:03 補充：
Answer 1 :

a = 0.3486220
b = 0.0520751
c = 0.1270818
d = - 0.2584682
y = 0.3715088
z = 0.1694424

2010-03-31 22:31:15 補充：
When a = - 0.0819553 :

- 0.0819553 + 4k = -0.3278212y
- 0.0819553 + y = 17k

Solve it : y = 0.1797836 , k = 0.0057546

so z = 4k = 0.0230184 , c = 3k = 0.0172638

By (10) : 0.0172638 = 7(- 0.0819553)b

b = - 0.0300927

By (9) : 0.0172638 + d = 12d(0.0057546)

d = - 0.0185444

2010-03-31 22:32:28 補充：
Answer 2 :

a = - 0.0819553
b = - 0.0300927
c = 0.0172638
d = - 0.0185444
y = 0.1797836
z = 0.0230184

(a+z)/y=4a
a+z=4ay
z=4ay-a

(b+z)/a=5c
b+z=5ca
b=5ca-z

(c+d)/c=4d
c+d=4dc
d=4dv-c

c/(a*b)=7
c=7(a*b)

a+y+z=7c
a=7c-y-z

c+a+y=5z
y=5z-a-c

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