若a+1⼀a=3,求a的1⼀2次方-a的-1⼀2次方及a的3⼀2次方-a-3⼀2次方的值

2024-12-24 12:15:29
推荐回答(1个)
回答1:

∵[a^(1/2)-a^(-1/2)]²
=a+1/a-2
=3-2
=1
∴ a^(1/2)-a^(-1/2)=1或-1

a^(3/2)-a^(-2/3)
=[a^(1/2)-a^(-1/2)][a+1/a-a^(1/2)·a^(-1/2)]
=±1·[3-1]
=±2