Solve \(2^{(2y+1)} – 5(2^y) + 2\) = 0
Explanation
\(2^{(2y+1)} - 5(2^y) + 2\) = 0
Let p = 2\(^y\)
\(2^{2y} (2^1) - 5(2^y)\) + 2 = 0
2p\(^2\) - 5p + 2 = 0
2p\(^2\) - p - 4p + 2 = 0
p (2p - 1) - 2(2p - 1) = 0
(p - 2)(2p - 1) = 0
p = 2 or \(\frac{1}{2}\)
p = 2\(^y\)
when p = 2
2\(^y\) = 2
y = 1
when p = \(\frac{1}{2}\)
2\(^y\) = \(\frac{1}{2}\)
2\(^y\) = 2\(^{-1}\)
y = -1
y = -1 or 1