- #1
Andolph23
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The Attempt at a Solution
2^x + 2^-x = 3
2^x + (1 / ((2^x)) = 3
(4^((x^2)) +1) / (2^x) = 3
(4^((x^2)) + 1) = 6^ x
What is the solution to 2^x + 2^-x = 3?
- Thread starter Andolph23
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Homework Help Overview
The discussion revolves around the equation 2^x + 2^-x = 3, which falls under the subject area of exponential equations. Participants are exploring various approaches to manipulate and solve the equation.
Discussion Character
- Exploratory, Mathematical reasoning, Problem interpretation
Approaches and Questions Raised
- Participants discuss rewriting the equation in different forms, such as expressing 2^-x as 1/(2^x) and considering substitutions like u = 2^x. There are attempts to manipulate the equation by multiplying both sides by 2^x, though some participants question the validity of certain steps.
Discussion Status
The discussion is active, with participants providing various insights and approaches. Some guidance has been offered regarding substitutions and methods to solve the equation, but there is no explicit consensus on the next steps or a complete solution yet.
Contextual Notes
Participants mention the need for the bases to be the same for certain manipulations, indicating a potential constraint in their approaches. There is also an acknowledgment of confusion regarding the steps taken in the problem-solving process.