# How many distinct integral value of $n$ satisfies the equation $2^{2n} - 3 \cdot (2^{n+2}) + 32 = 0$?

How many distinct integral value of $n$ satisfies the equation $2^{2n} - 3 \cdot (2^{n+2}) + 32 = 0$ ?

-
add comment

## 2 Answers

HINT: make the substitution $x=2^{n}$ This will reduce your equation to a quadratic.

-
Thanks for the hint, So it boils to $X^2 -12x +32 = 0$ solving ${{x -> 4}, {x -> 8}}$ which gives n=2,3. Hence, 2 distinct integral value of n is possible. –  Quixotic Oct 28 '10 at 5:16
Yep! That's what I got as well :) –  WWright Oct 28 '10 at 5:17
add comment

You should be able to prove a fairly small limit on n. Think about the fact that 3<2^2. Then you can just try them all up to there.

-
add comment