數學題1條

4/u - 5/v = 8 .................(1)
2/u - 7/v = 20................ (2)
from (1)
4v-5u=8uv
from (2)
2v-7u=20uv
so we know that
2.5(4v-5u)=2v-7u
10v-12.5u=2v-7u
8v=5.5u
v=(55/80)u
sub back into (1)
4/u - 5/v = 8
4/u - 5/[(55/80)u] = 8
4/u - 400/[(55u] = 8
-36/11=8u
u=-9/22
v=(55/80)u=-9/32

It will be more elegant if you let x = 1/u and y = 1/v.
Then the equation becomes
4x - 5y = 8 ----------(3)
2x - 7y = 20 -----------(4)

Solving (3), (4), you have y = -32/9 and x = -22/9
So u = -9/22, v = -9/32

v=(55/80)u=-9/32

multiply each equation with uv .
4v-5u=8uv.................(1)
2v-7u=20uv................(2)

(2) * 2

4v-14u=40uv (3)

(1) - (3)
9u= -32uv (Divide u )
9= -32v
v= -32/9

(3) - (1)
-9v=32uv (Divide v )
-9u=32
u=32/-9

2006-11-27 17:47:13 補充：
v= -32/9u= -32/9 or 32/-9