Simple exponential equation | 2^x + 2^-x =17/4
Updated: January 22, 2025
Summary
The video presents an introduction to exponential equations and a method to simplify them by cleverly rewriting terms. By manipulating the equation and rearranging terms, a quadratic equation is obtained for easy factorization. The video then delves into finding possible solutions for x by solving the quadratic equation through careful consideration of different cases. The video is a great resource for individuals looking to enhance their understanding of exponential equations and solving for unknown variables.
Introduction and Equation Simplification
Introduction to the exponential equation provided by a Facebook follower and simplifying the equation by rewriting 2^x as 1 / 2^(-x).
Multiplying Terms and Rearranging
Multiplying every term by 2^x*4 to simplify the equation and rearrange the terms for easier factorization.
Factorization of Quadratic Equation
Factorizing the quadratic equation obtained after rearranging the terms and finding the possible solutions for x.
Solving for x
Solving the quadratic equation to find the possible values for x by considering the different cases and simplifying the expressions.
FAQ
Q: What is the purpose of rewriting 2^x as 1 / 2^(-x) in the exponential equation?
A: Rewriting 2^x as 1 / 2^(-x) helps in simplifying the equation and making it easier to work with.
Q: Why is it necessary to multiply every term by 2^x*4 in the given equation?
A: Multiplying every term by 2^x*4 is done to simplify the equation and prepare it for factorization.
Q: What is the significance of rearranging the terms in the equation before factorization?
A: Rearranging the terms in the equation makes it easier to factorize and find the solutions for x.
Q: Why is it important to find the possible solutions for x in the quadratic equation obtained after rearranging the terms?
A: Finding the possible solutions for x helps in determining the different values that satisfy the equation.
Q: How is the quadratic equation solved to find the possible values for x?
A: The quadratic equation is solved by considering different cases and simplifying the expressions to determine the values of x.
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