作业帮f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
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f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
1.换元,令x+y=m & x-y=n
则x=(m+n)/2,y=(m-n)/2
2.回代,得f(m,n)=[[(m+n)/2]^2-[(m-n)/2]^2]/[2*(m-n)/2*(m+n)/2]=2mn/(m^2-n^2)
3.m,n是符号变量 可以改写成x,y 则,f(x,y)=2xy/(x^2-y^2)
f(x+y,x-y)=(x^2-y^2)/2xy=2（x+y）(x-y)/((x+y)^2-(x-y)^2)
f(x,y)=2xy/(x^2-y^2)
令x+y=u,x-y=v,即有x=(u+v)/2,y=(u-v)/2,带入即可得f(u,v)的表达式,即是
将f(u,v)表达式中的u,v换成x,y即得f(x,y)的表达式。
令x+y=a,x-y=b,解出来x,y用a,b表示，带入后边
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