高数不懂了,f(x+y,y/x)=x2+y2,求(x,y)
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高数不懂了,
f(x+y,y/x)=x2+y2,求(x,y)
f(x+y,y/x)=x2+y2,求(x,y)
![高数不懂了,f(x+y,y/x)=x2+y2,求(x,y)](/uploads/image/z/17347804-52-4.jpg?t=%E9%AB%98%E6%95%B0%E4%B8%8D%E6%87%82%E4%BA%86%2Cf%28x%2By%2Cy%2Fx%29%3Dx2%2By2%2C%E6%B1%82%EF%BC%88x%2Cy%EF%BC%89)
令m=x+y,n=y/x,解得:
x=m/(n+1);y=mn/(n+1)
代入f(x+y,y/x)=x2+y2得:
f(m,n)=(m/(n+1))^2+(mn/(n+1))^2=m^2(n^2+1)/(n+1)^2
所以,f(x,y)=x^2(y^2+1)/(x+1)^2
x=m/(n+1);y=mn/(n+1)
代入f(x+y,y/x)=x2+y2得:
f(m,n)=(m/(n+1))^2+(mn/(n+1))^2=m^2(n^2+1)/(n+1)^2
所以,f(x,y)=x^2(y^2+1)/(x+1)^2
高数:已知f(x+y,y)=x^2+y^2,求f(x,y)
我做对了吗.x2(x-y)+y2(y-x)= x2(x-y)-y2(x-y)=x2-y2=(x+y)(x-y)
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