分类：教育/科学-学习帮助
问题：已知a^(1/2)
求：(1) a^(1/2)+a^(-1/2)(2) a^(3/2)-a^(-3/2)
回答：a^(1/2)-a^(-1/2)=3:  a^(1/2)-1/a^(1/2)=3
a-3a^(1/2)-1=0, a=3a^(1/2)+1
a^(1/2)=(3+13^(1/2))/2

(1):
a^(1/2)+a^(-1/2)=(a+1)/a^(1/2)=(3a^(1/2)+2)/a^^(1/2)
=3+2/((3+13^(1/2))/2)=3+4(13^(1/2)-3)/4=13^(1/2)

(2):
a^(3/2)-a^(-3/2)=(a^(1/2)-a^(-1/2))(a+1+a^(-1))
=3((a^(1/2)-a^(-1/2))^2+3)
=3(3^2+3)=36