+ / -檢視主題
由 scsnake 於 星期四 六月 12, 2003 10:52 pm
我也看不懂題目∼
由 --- 於 星期四 六月 12, 2003 10:45 pm
隨便的題目, 隨便的解答
由 --- 於 星期四 六月 12, 2003 4:29 pm
x+y+z
= 1/x+1/y+1/z =(xy+xz+yz )/xyz
= xy+xz+yz
xyz=1
let m=xy=1/z
let x+y=n
z=1/m
n+1/m
= m+n/m
mn+1=mm+n
mm-nm +n-1=0
m=(n-1) or 1
(1) if m=xy=1
xy+2z=β=1+2=3
x+y 隨便(>=2 or <=-2)
(2) if m=n-1
xy=x+y-1
(x-1)(y-1)=0
xy+2z=y+2/y
to maximize m+2/m,
if m>sqrt(2), we should maximize m
that is, maximize n-1
==> n=infinite, m=infinite, α =infinite, β=infinite
= 1/x+1/y+1/z =(xy+xz+yz )/xyz
= xy+xz+yz
xyz=1
let m=xy=1/z
let x+y=n
z=1/m
n+1/m
= m+n/m
mn+1=mm+n
mm-nm +n-1=0
m=(n-1) or 1
(1) if m=xy=1
xy+2z=β=1+2=3
x+y 隨便(>=2 or <=-2)
(2) if m=n-1
xy=x+y-1
(x-1)(y-1)=0
xy+2z=y+2/y
to maximize m+2/m,
if m>sqrt(2), we should maximize m
that is, maximize n-1
==> n=infinite, m=infinite, α =infinite, β=infinite
[數學]在來一題~~
由 Searchtruth 於 星期二 六月 10, 2003 8:01 pm
x+y+z = 1/x+1/y+1/z = xy+xz+yz
問: 當 x+y=α , xy+2z=β ,有最大值 (α , β)=?
問: 當 x+y=α , xy+2z=β ,有最大值 (α , β)=?