Question

How do you rewrite this expression?

Answer 1

what will you get if you expand those parentheses
\[\Big(e^t+A\Big)^2=\]

Answer 2

e^t+2Ae^t + A^2

Answer 3

not quite
check that first term

Answer 4

e^2t+2Ae^t + A^2

Answer 5

right so you need to find the A, that satisfies

e^2t + 2 + e^-2t = e^2t + 2Ae^t + A^2

i.e. the A that solve both

2 = 2Ae^t
and
e^-2t = A^2

Answer 6

what is A? (a function of t)

Answer 7

e^-t :s

Answer 8

YES!

Answer 9

:D

Answer 10

let's check it
\[\left(e^t+e^{-t}\right)^2\\
=\left(e^t+e^{-t}\right)\left(e^t+e^{-t}\right)\\
=e^t\left(e^t+e^{-t}\right)+e^{-t}\left(e^t+e^{-t}\right)\\
=e^{2t}+1+1+e^{-2t}\\
=e^{2t}+2+e^{-2t}\]

Answer 11

Awesome! thanks!