數學题一問~

上面個兩個都冇睇問題
個問題係問個value

個答案應該係3+√(7)

x+y+z=7
(x+y+z)²=49
x²+y²+z²+2xy+2yz+2zx=49
x²+y²+z²+16=49
x²+y²+z²=33

x,y,z are roots to equation w³-7w²+8w-w=0
(w-1)(w²-6w+2)=0
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w=1 3±√(7)

所以答案係3+√(7)

唔知仲有冇其他方法

2007-12-07 13:19:40 補充：
其實仲有另外一個方法y z = 7 - xyz = 2/xxy yz zx = 8x(y z ) yz = 8x ( 7 - x ) 2/x = 87x - x² 2/x = 8x³ -7x² 8x -2 = 0x = 1, 3 √(7), 3-√(7)最大個數係3 √(7),

x+y+z=7
x=7-y-z

xy+yz+zx=8
xy+zx+yz=8
x(y+z)=8-yz
x=8-yz/y+z

xyz+2
x=2-yz

x= 7-y-z

x(y+z) +yz = 8
x=8-yz / y+

x=2/yz