Question

一道高一数学题（求详细过程）4设X的1/2次方+X的-1/2次方=3,则（X的3/2次方+X的-3/2次方+2）/（X的

Answer 1

x^(1/2)+x^(-1/2)=3

两边平方

x+1/x+2=9

x+1/x=7

x^(3/2)+x^(-3/2)+2

=[x^(1/2)+x^(-1/2)]*(x-1+1/x)

=3*(7-1)

=18

x^2+1/x^2+3

=(x+1/x)^2-2+3

=50

原式=18/50=9/25