设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)
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设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)答:f(x+y,x-
设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)
设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)
设f(x+y,x-y)=x^2+y^2-x*y求f(x,y)
答:
f(x+y,x-y)=x^2+y^2-xy
设x+y=a,x-y=b
解得:x=(a+b)/2,y=(a-b)/2
所以:
f(a,b)=(a+b)^2 /4+(a-b)^2 /4-(a+b)(a-b)/4
f(a,b)=(1/4)*(a^2+2ab+b^2+a^2-2ab+b^2-a^2+b^2)
f(a,b)=(1/4)*(a^2+3b^2)
所以:
f(x,y)=(x^2+3y^2)/4
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