Simultaneous Exponential Equations | Math Olympiad Challenge

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Welcome, fellow math aficionados, to an exhilarating episode of the Math Olympiad Challenge!

Today, we're delving into the fascinating realm of Simultaneous Exponential Equations, where we'll unravel the complexities of mathematical puzzles that are bound to ignite your intellectual curiosity.

The central enigma awaiting our attention is a pair of equations: 6^a + 6^b = 42 and a + b = 3. Buckle up as we embark on a journey to decipher these simultaneous exponential equations, where the synergy of exponents and variables creates a captivating mathematical tapestry.

Throughout this tutorial, we'll dissect the problem step by step, demystifying the intricacies of exponential equations and showcasing strategic methods for solving them concurrently. Whether you're gearing up for a Math Olympiad, honing your problem-solving prowess, or simply relishing the thrill of mathematical challenges, this video is tailor-made for you.

Join me as we explore the foundations of exponential equations, understanding the nuances of their behavior and how they intertwine within the context of simultaneous solutions. I'll provide clear explanations, pro tips, and insightful strategies that will not only help you crack this specific problem but also empower you with a broader understanding of exponential equations.

Now, let's unlock the potential of our mathematical minds with the following keywords:
Simultaneous Exponential Equations
Solving Simultaneous Exponential Equations
Exponential Equations
Solving Exponential Equations

Are you ready to elevate your mathematical acumen? Hit that play button, dive into the challenge with me, and embark on a journey of mathematical discovery. Don't forget to hit the like button if you enjoy the video, subscribe for more exhilarating challenges, and share your brilliant solutions in the comments below.

Together, let's conquer the world of simultaneous exponential equations and showcase our prowess in the realm of mathematical excellence.

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My intuitive approach is to note that 42 = 6^2 + 6^1 and comparing that with 6^a + 6^b and a + b = 3, leads to a = (1, 2) and b = (2, 1)

wes
Автор

6^a+6^b=42
a+b=3 b=3-a

6^a+6^(3-a)=42
6^a+[216/(6^a)]=42
(6^a)^2+216=42(6^a)
x^2+216=42x
x^2-42x+216=0
(x-36)(x-6)=0

x-36=0
x=36
6^a=6^2
a=2 ❤
2+b=3
b=1 ❤

x-6=0
x=6
6^a=6^1
a=1 ❤
1+b=3
b=2 ❤

ChavoMysterio