Let's Solve A Challenging Exponential Equation for All Reals
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- Опубліковано 26 чер 2024
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Let's Solve A Challenging Exponential Equation for All Reals
In this video, we tackle a challenging exponential equation and solve it for all real numbers. Join us as we explore different techniques and strategies to find the solution. Whether you're a math enthusiast or preparing for exams, this step-by-step tutorial will enhance your problem-solving skills and deepen your understanding of exponential functions. Don't forget to like, subscribe, and hit the bell icon for more math challenges and tutorials!
Topics covered:
Exponential equations
How to solve exponential equations
Algebra
Algebraic identities
Exponential Equation
Math Olympiad preparation
Math Olympiad training
Exponent laws
Quadratic equation
Factorization
Algebraic manipulations
Real solutions
Timestamps:
0:00 Introduction
1:40 Exponent laws
2:36 Substitutions
5:42 Algebraic identities
9:11 Solutions
9:25 Verification
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Thanks for Watching !!
@infyGyan
Nice solution.
Other approach: AM-GM: (a⁴+b⁴+c⁴+1)/4 ≥ (a⁴∙b⁴∙c⁴∙1)^(¼) = abc. Equality holds only when all four terms are equal ie. a⁴=b⁴=c⁴=1. Hence x=0.
A wonderful introduction and explanation.....x=0
Great method 😊❤❤
I appreciate the very clever algebraic manipulations. But x = 0 is obvious by inspection. Any expression of similar exponential form in which the numerator and denominator are equal if x = 0 could have been posed as a problem. Proving uniqueness of x = 0 may be a challenge, though.
X=0. By inspection of constraints, it is the only possible solution.
X=0
At 6.0 minutes, each individual bracket is equal to 0 is one possibility and that leads to the solution, x = 0.
But there are three other possibilities that I will try to solve, when one bracket is 0, other two brackets can have opposite sign.
But square cannot be negative hence all equal to 0
x=0 is a solution 😊❤