A Nice Exponential Equation | Math Olympiad Training

A Nice Exponential Equation | Math Olympiad Training
Welcome to another intriguing math challenge! In this video, we dive into a beautiful exponential equation from the Math Olympiad Prep. This problem will test your understanding of exponential functions and your problem-solving abilities.
Are you ready to take on this challenge? Watch the video, attempt to solve the equation on your own, and then compare your solution with ours. Don’t forget to share your approach and solution in the comments below!
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Topics covered:
Exponential equations
How to solve exponential equations?
Algebra
Exponents
Factorization
Properties of exponents
Algebraic identities
Radicals
Cubic equations
Math Olympiad preparation
Math Olympiad training
Exponent laws
Real solutions
Additional Resources:
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• An Interesting Factori...
• Can You Solve This Exp...
#exponentialequations #cubicequation #mathematics #math #matholympiad #problemsolving #exponents #radical #algebra
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Thanks for Watching !!

[@mohammedsaysrashid3587]

It was a wonderful introduction and clearly explaining....thanks, Sir 🙏....x=4

[@user-kp2rd5qv8g]

Let 2^(x/2) = t. Then, the given equation is equivalent to t^3-2t^2-32=0 which has t=4 as the only real solution. Thus, x/2 = 2 > x=4.

[@samah9496]

2^(3x/2)-2×2^x-32=0
X=2^(x/2)
X³-2X²-32=0
Pour X=4
4³-2×4²-32=0
(X-4)(X²+2X+8)=0
X²+2X+8=0 solution complexe
S={4}
X=2^(x/2)=4=2²
x/2=2
x=4

[@user-ny6jf9is3t]

χ=4

[@tejpalsingh366]

X= 4 only real soln
Rest r complex

[@boy-bf3si]

X=4 is answer

[@kassuskassus6263]

x=4

[@walterwen2975]

A Nice Exponential Equation: (√2)ˣ - 2⁵⁻ˣ = 2, x ϵR; x = ?
(√2)ˣ > 0, No complex and/or imaginary value root
(√2)ˣ - 2⁵⁻ˣ = (√2)ˣ - 2⁵/2ˣ = (√2)ˣ - 2⁵/(√2ˣ)² = 2, [(√2)ˣ]³ - 2(√2ˣ)² - 2⁵ = 0
Let: y = (√2)ˣ, [(√2)ˣ]³ - 2(√2ˣ)² - 2⁵ = y³ - 2y² - 32 = 0; y = (√2)ˣ > 0, y ϵR
(y³ - 4y²) + 2(y² - 16) = y²(y - 4) + 2(y + 4)(y - 4) = (y - 4)(y² + 2y + 8) = 0
y² + 2y + 8 > 0; y - 4 = 0, y = 4, (√2)ˣ = 2ˣ⸍² = 4 = 2², x/2 = 2; x = 4
Answer check:
(√2)ˣ - 2⁵⁻ˣ = 2⁴⸍² - 2⁵⁻⁴ = 4 - 2 = 2; Confirmed
Final answer:
x = 4

[@RealQinnMalloryu4]

(2x)^2=2x^2 ➖ (2 x)^5= 32x^5 {4x^2 ➖ 32x^5}= 28x^3 3^8x^3 1^2^3x^3 2^3^1x^3^1 21^1x^3^1 2x^3 (x ➖ 3x+2)

[@user-kt1dm9jz5t]

x=4

[@RajeshKumar-wu7ox]

X=4

[@RajeshKumar-wu7ox]

And another solution is comlex