解方程 3^x - 3^-x = 80/9

问题描述:

解方程 3^x - 3^-x = 80/9

3^x=9
X=2

3^x - 3^-x = 80/9
(9*3^2x+1)(3^3x-9)=0
则9*3^2x+1=0或3^3x-9=0
从而3^3x=9
x=2

x=2

X=5/36

设t=3^x
3^x - 3^-x = 80/9
t - 1/t =80/9
9t^2 - 80t - 9=0
(9t+1)(t-9)=0
又t>0
t=9
3^x=9=3^2
x=2