设f(x+y,x-y)=(x²-y²)/2xy ,则f(x,y)=?

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设f(x+y,x-y)=(x²-y²)/2xy,则f(x,y)=?设f(x+y,x-y)=(x²-y²)/2xy,则f(x,y)=?设f(x+y,x-y)=(x

设f(x+y,x-y)=(x²-y²)/2xy ,则f(x,y)=?
设f(x+y,x-y)=(x²-y²)/2xy ,则f(x,y)=?

设f(x+y,x-y)=(x²-y²)/2xy ,则f(x,y)=?
令x+y=2a
x-y=2b
所以2x=2a+2b
x=a+b
2y=2a-2b
y=a-b
f(2a,2b)
=(x+y)(x-y)/2xy
=(a+b+a-b)(a+b-a+b)/2(a+b)(a-b)
=2a*2b/2(a^2-b^2)
=2a*2b*2/(4a^2-4b^2)
=2a*2b*2/[(2a)^2-(2b)^2]
∴f(x,y)=2xy/(x^2-y^2)