Question

已知f（x）=a^x-a^-x,g(x)=a^x+a^-x(a>0,且a不等于0）

Answer 1

g(x)g(y)=(a^x+a^-x)(a^y+a^-y)=a^(x+y)+a^(x-y)+a^-(x-y)+a^-(x+y)=8;-----(1)

f(x)f(y)=(a^x-a^-x)(a^y-a^-y)=a^(x+y)-a^(x-y)-a^-(x-y)+a^-(x+y)=4------(2);

(1)+(2):

2[a^(x+y)+a^-(x+y)]=12;

g(x+y)=a^(x+y)+a^-(x+y)=6;

(1)-(2):

2[a^(x-y)+a^-(x-y)]=4;

g(x-y)=[a^(x-y)+a^-(x-y)]=2;

g(x+y)/g(x-y)=6/2=3