求下列各函数表达式f(x+y,y⼀x)=x∧2–y∧2,求f(x,y).

2025-02-26 04:36:26
推荐回答(1个)
回答1:

若f(x,y)=x^2-y^2,
则f(x+y,y/x)=(x+y)^2-(y/x)^2

若f(x+y,y/x)=x^2-y^2
令a=x+y , b=y/x
则y=bx, a=x+bx, 得:
x=a/(1+b),y=ab/(1+b)
故f(a, b)=a^2/(1+b)^2 -(ab)^2/(1+b)^2=a^2/(1+b)^2*(1-b^2)=a^2(1-b)/(1+b)
即f(x, y)=x^2(1-y)/(1+y)

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