Question

已知 x的1/2次幂+x的-1/2次幂=2 求x的3/2次幂 + x的-3/2次幂 比上 x的1/2次幂+x的-1/2次

Answer 1

x^0.5+1/x^0.5=2

x+1/x=(x^0.5+1/x^0.5)^2-2=2

(x^1.5+1/x^1.5)/(x^0.5+1/x^0.5)=(x^0.5+1/x^0.5)(x+1/x-1)/(x^0.5+1/x^0.5)=x+1/x-1=1