已知f(x)=e^x+e^(-x),g(x)=e^x-e^(-x)且f(x)*f(y)=4,g(x)*g(y)=8,求f(x+y)/f(x-y)的值。
热心网友
4=f(x)f(y)=[e^x+e^(-x)][e^y+e^(-y)]=e^(x+y)+e^[-(x+y)]+e^(x-y)+e^[-(x-y)]8=g(x)g(y)=[e^x-e^(-x)][e^y-e^(-y)]=e^(x+y)+e^[-(x+y)]-e^(x-y)-e^[-(x-y)]== e^(x+y)+e^[-(x+y)] = 6, e^(x-y)+e^[-(x-y)] = -2== f(x+y)/f(x-y) = {e^(x+y)+e^[-(x+y)]}/{e^(x-y)+e^[-(x-y)]} = -3