已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?
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已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)
已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?
已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?
已知F(X+Y,X-Y)=X^2*Y+X*Y^2,则F(X,Y)=?
令m= X+Y n=X-Y
有X = (m+n)/2 Y = (m-n)/2
代入F(X+Y,X-Y)=X^2*Y+X*Y^2
得 F(m,n)= 1/4 * (m+n)^2 * (m-n)/2 + 1/4 * (m-n)^2 * (m+n)/2
= 1/8 * [(m^2-n^2 )(m+n) + (m^2-n^2)(m-n)]
= 1/8 * (m^2-n^2) * 2m
= m(m^2-n^2)/4
所以F(X,Y)=X(X^2-Y^2)/4
F(X,Y)=X(X^2-Y^2)/4
只需要令s=X+Y,t=X-Y，代入上式解出F(s,t)即可
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