已知函数f(x)=e^x-e^-x,g(x)=e^x+e^-x
(1)求[f(x)]^2-[g(x)]^2的值（2）设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x-y)...
(1)求[f(x)]^2-[g(x)]^2的值（2）设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x-y)
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f(x)+g(x)=2*e^x (f(x)+g(x))^2= 4*e^2x
f(x)g(x)=e^2x-e^-2x {f(x)}^2+{g(x)}^2=2e^2x+2e^-2x f(x)f(y)=[e^x-e^-x][e^y-e^-y]
=e^(x+y)-e^(x-y)-e^[-(x-y)]+e^[-(x+y)]
=g(x+y)-g(x-y)=4
g(x)g(y)=[e^x+e^-x][e^y+e^-y]
=e^(x+y)+e^(x-y)+e^[-(x-y)]+e^[-(x+y)]
=g(x+y)+g(x-y)=8
解得:
g(x+y)=6
g(x-y)=2
因此:
g(x+y)/g(x-y)=3
f(x)g(x)=e^2x-e^-2x {f(x)}^2+{g(x)}^2=2e^2x+2e^-2x f(x)f(y)=[e^x-e^-x][e^y-e^-y]
=e^(x+y)-e^(x-y)-e^[-(x-y)]+e^[-(x+y)]
=g(x+y)-g(x-y)=4
g(x)g(y)=[e^x+e^-x][e^y+e^-y]
=e^(x+y)+e^(x-y)+e^[-(x-y)]+e^[-(x+y)]
=g(x+y)+g(x-y)=8
解得:
g(x+y)=6
g(x-y)=2
因此:
g(x+y)/g(x-y)=3
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