f（x+y,y/x）=x^2-y^2，求f（x,y）=?
答案:3 悬赏:50 手机版
解决时间 2021-11-29 11:24
- 提问者网友：暗中人
- 2021-11-28 22:27
f（x+y,y/x）=x^2-y^2，求f（x,y）=?
最佳答案
- 五星知识达人网友：青尢
- 2021-11-28 23:07
y=sx
x=t-y=t-sx
(s+1)x=t
x=t/(s+1)
y=sx=st/(s+1)
f(x+y,y/x)=x²-y²
f(t，s)=[t/(s+1)]²-[st/(s+1)]²
=t²/(s+1)²-s²t²/(s+1)²
=(t²-s²t²)/(s+1)²
=t²(1-s²)/(1+s)²
=t²(1+s)(1-s)/(1+s)²
=t²(1-s)/(1+s)
将t换成x，s换成y，得
f(x，y)=x²(1-y)/(1+y)
x=t-y=t-sx
(s+1)x=t
x=t/(s+1)
y=sx=st/(s+1)
f(x+y,y/x)=x²-y²
f(t，s)=[t/(s+1)]²-[st/(s+1)]²
=t²/(s+1)²-s²t²/(s+1)²
=(t²-s²t²)/(s+1)²
=t²(1-s²)/(1+s)²
=t²(1+s)(1-s)/(1+s)²
=t²(1-s)/(1+s)
将t换成x，s换成y，得
f(x，y)=x²(1-y)/(1+y)
全部回答
- 1楼网友：酒醒三更
- 2021-11-29 01:29
令a=x+y,b=y/x,得x=a/(1+b),y=ab/(1+b)
故f(a,b)=x^2-y^2=[a/(1+b)]^2-[ab/(1+b)]^2
故f(a,b)=x^2-y^2=[a/(1+b)]^2-[ab/(1+b)]^2
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