解方程组4x^2/(1+4x^2)=y,4y^2/(1+4y^2)=z,4z^2/(1+4z^2)=x今晚要
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解方程组4x^2/(1+4x^2)=y,4y^2/(1+4y^2)=z,4z^2/(1+4z^2)=x今晚要解方程组4x^2/(1+4x^2)=y,4y^2/(1+4y^2)=z,4z^2/(1+4z
解方程组4x^2/(1+4x^2)=y,4y^2/(1+4y^2)=z,4z^2/(1+4z^2)=x今晚要
解方程组4x^2/(1+4x^2)=y,4y^2/(1+4y^2)=z,4z^2/(1+4z^2)=x
今晚要
解方程组4x^2/(1+4x^2)=y,4y^2/(1+4y^2)=z,4z^2/(1+4z^2)=x今晚要
得到两组解
0,0,0
0.2119268995,0.2119268995,0.2119268995
4x2/(1+4x2)=y...①
4y2/(1+4y2)=z...②
4z2/(1+4z2)=x...③
当x=0时,各等式显然成立
当x≠0时,①+②+③得:
x+y+z=4x2/(1+4x2)+4y2/(1+4y2)+4z2/(1+4z2) ≤4x2/4x+4y2/y+4z2/z=x+y+z ,当且仅当x=y=z=1/2时等号成立
...
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4x2/(1+4x2)=y...①
4y2/(1+4y2)=z...②
4z2/(1+4z2)=x...③
当x=0时,各等式显然成立
当x≠0时,①+②+③得:
x+y+z=4x2/(1+4x2)+4y2/(1+4y2)+4z2/(1+4z2) ≤4x2/4x+4y2/y+4z2/z=x+y+z ,当且仅当x=y=z=1/2时等号成立
经检验得知x=1/2,y=1/2,z=1/2是方程组的解.
综上
x=0
y=0
z=0
或
x=1/2
y=1/2
z=1/2
收起
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