a^(1/2)+a^(-1/2)=3，則(a^(-3/2)+

a^(1/2)+a^(-1/2)=3_________√a+1/√a=3______(√a+1/√a)²=3²_________a+2+1/a=9___________a+1/a=7 ---(1)________(a+1/a)²=7²_______a²+2+1/a²=49_________a²+1/a²=47 ---(2) _________a³+1/a³=(a+1/a)(a²-1+1/a²)By (1) & (2), _________a³+1/a³=(7)(47-1)_________a³+1/a³=322 ---(3) ____(√a³+1/√a³)²=a³+2+1/a³By (3), ____(√a³+1/√a³)²=322+2=324_______√a³+1/√a³=√324=18 ---(4) [a^(-3/2)+a^(3/2)]/[a^2+a^(-2)]=(√a³+1/√a³)/(a²+1/a²)By (2) & (4), =18/47

a^(1/2)+a^(-1/2)=3，則(a^(-3/2)+a^(3/2))/(a^2+a^(-2))之值為?Sol: 令X= a^(1/2) 則1/X = a^(-1/2)且X+1/X=3 (X+1/X)^2=9 X^2+2+1/X^2=9 X^2+1/X^2=7(X+1/X)(X^2+1/X^2)=3*7=21(X^3+1/X^3)+(X+1/X)= (X^3+1/X^3)+3=21(X^3+1/X^3)=18(X^2+1/X^2)^2=7^2=49X^4+1/X^4+2=49X^4+1/X^4=49-2=47(a^(-3/2)+a^(3/2))/(a^2+a^(-2))=(1/X^3+X^3)/(X^4+1/X^4)=18/47