Challenge Accepted: Can You Crack This Radical Equation?

Challenge Accepted: Can You Crack This Radical Equation?

Welcome to the ultimate math challenge! Think you have what it takes to crack this radical equation? Join us as we delve into the world of mathematics and put your problem-solving skills to the test. Whether you're a math whiz or just looking for a fun challenge, this is the place to be. Get ready to sharpen your mind and tackle the Radical Equation Challenge head-on! Are you up for it?

Topics Covered:
1. Understanding the basics of radical equations.
2. Analyzing the unique properties and substitution of the given equation.
3. Step-by-step approach to solving the radical equation.
4. Tips and tricks for handling tricky radicals like a pro.
5. Algebraic identities and manipulations while solving equations.

Timestamps:

0:00 Introduction
1:20 Substitution
2:08 Solving system of equations
4:38 Complex solutions
5:26 Solving cubic equations
6:25 Synthetic division method
7:16 Quadratic equation
7:45 Quadratic formula
8:35 Solutions
9:01 Verification

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Thanks for Watching!
@infyGyan

[ranshen]

RHS = 2 ∛(20x + 16). Let this be 2 t.
Then we get symmetric equations
x³ = 20t + 16,
t³ = 20x + 16.
So t = x, and
0 = x³ – 20x – 16 = (x + 4) (x² – 4x – 4),
leading to
x = –4, or 2 ± 2√2.