一道数学题,实在不懂,
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一道数学题,实在不懂,
(y+z-x)/x=(x+z-y)/y=(x+y-z)/z 求[(x+y)(y+z)]/xz的值(分数线用 / 代替)
(y+z-x)/x=(x+z-y)/y=(x+y-z)/z 求[(x+y)(y+z)]/xz的值(分数线用 / 代替)
![一道数学题,实在不懂,](/uploads/image/z/16017095-47-5.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%AE%9E%E5%9C%A8%E4%B8%8D%E6%87%82%2C)
设(y+z-x)/x=(x+z-y)/y=(x+y-z)/z=k
{y+z-x=kx (1)
{x+z-y=ky (2)
{x+y-z=kz (3)
(1)+(2)+(3)得
x+y+z=k(x+y+z)
k=1或x+y+z=0
(1)+(2)得
2z=k(x+y) (4)
(2)+(3)得
2x=k(y+z) (5)
(4)×(5)得
4xz=k²(x+y)(y+z)
当k=1时
[(x+y)(y+z)]/xz=4/k²=4
当x+y+z=0时
[(x+y)(y+z)]/xz=(-z)(-x)/xz=-1
{y+z-x=kx (1)
{x+z-y=ky (2)
{x+y-z=kz (3)
(1)+(2)+(3)得
x+y+z=k(x+y+z)
k=1或x+y+z=0
(1)+(2)得
2z=k(x+y) (4)
(2)+(3)得
2x=k(y+z) (5)
(4)×(5)得
4xz=k²(x+y)(y+z)
当k=1时
[(x+y)(y+z)]/xz=4/k²=4
当x+y+z=0时
[(x+y)(y+z)]/xz=(-z)(-x)/xz=-1