3^x + 3^-x = 82/9
3^x + 1/3^x = 82/9
(3^2x + 1)/3^x = 82/9
clearly, x=2, but let's go on.
9(3^2x + 1) = 82*3^x
9*3^2x - 82*3^x + 9 = 0
think of this as 9u^2-82u+9, and you get
(9*3^x - 1)(3^x - 9) = 0
3^x = 9 or 1/9
x = 2 or -2
aha. an unexpected solution!
EXPONENTIAL EQUATION
Find the X
3^x - 82/9 = -3^-x
2 answers
Thank you so much. It really helps me 😂