推 bn51401 :3? 07/02 01:47
→ coolcomm :x+y+z=0 ? 07/02 10:00
推 czk0622 :有兩個解吧 x/y=1 或 x/y=w 或 x/y=w^2 07/02 10:59
→ CaptainH :令x/y=y/z=z/x=k. 則 x=yk=zk^2=xk^3, x≠0所以k^3=1 07/02 12:01
→ CaptainH :k=1,w,w^2. 分別代入(x+y+z)/(x-y+z) = 0 or 3 07/02 12:04
推 nicewine1 :x/y=y/z=z/x = (x+y+z)/(y+z+x) = 1->x=y=z 07/02 19:12
推 nicewine1 :(x+y+z)/(x-y+z) = (1+1+1)/(1-1+1)=3 07/02 19:18
推 thisday :樓上的方法不錯 但會漏掉一個答案 07/02 20:06
→ thisday :漏掉的那個答案就是x+y+z=0的情況! 07/02 20:06
推 nicewine1 :x=k*y=k^2*z=k^3*x->k^3=1->k^3-1=0->k=1,w,w^2 07/02 22:08
推 nicewine1 :x+y+z可能為0嗎 07/02 22:17
推 nicewine1 :1+w+w^2=0??? 07/02 22:22
→ bibo9901 :樓上, k^3-1 = (k-1)(k^2+k+1) 07/02 23:24
→ thisday :1+w+w^2=0 07/03 00:12