"This equation — \(4^x - 5(2^x) + 4 = 0\) — doesn't look like anything you already know how to solve. But it's wearing a disguise. Can your group unmask it?"
Rewrite \(4^x\) so it's written in terms of \(2^x\).
Substitute this back into the equation. What do you notice?
Turn it into an equation you already know how to solve. What kind of equation is it?
Solve the equation you found in Phase 1.
Reverse your substitution to find \(x\).
Check each value of \(x\) in the original equation.
Use your method on \(9^x - 4(3^x) - 45 = 0\).
Before finishing: is every value you found actually possible?
Use your method on \(2^x+2^{-x}=1\). It won't look like a quadratic yet — can you find a way to make it one?
Solve it — what happens? What does that tell you about the original equation?
Without the discriminant, explain directly why \(2^x+2^{-x}\) can never equal 1.