【20點】簡化問題

圖片參考：http://bbs-mychat.com/attach/Fid_686/686_700258.jpg


a = √ [ x² + (xy/(x+z))²] + √ [ z² + (yz/(x+z))²]

a = √ [ x²( (x+z)² + y² ) / (x+z)² ] + √ [ z²( (x+z)² + y² ) / (x+z)² ]

a = |x / (x+z)| √ [ (x+z)² + y² ] + |z / (x+z)| √ [ (x+z)² + y² ]

a = √ [ (x+z)² + y² ]



2010-10-14 18:22:49 補充：
(當 x / (x+z) > 0 及 z / (x+z) > 0)

2010-10-14 22:28:22 補充：
官方小雲_紫苑小魔聖 ( 中學級 1 級 )

Don't copy my answer!!

when x / (x+z) or z / (x+z)> 0 ,
a = √ [ x² + (xy/(x+z))²] + √ [ z² + (yz/(x+z))²]
= √ [ x²( (x+z)² + y² ) / (x+z)² ] + √ [ z²( (x+z)² + y² ) / (x+z)² ]
= |x / (x+z)| √ [ (x+z)² + y² ] + |z / (x+z)| √ [ (x+z)² + y² ]
= √ [ (x+z)² + y² ]