A Nice Radical Equation | Algebra | Math Olympiad Prep

A Nice Radical Equation | Algebra | Math Olympiad Prep

Get ready for a thrilling algebra challenge with this intriguing radical equation! Perfect for Math Olympiad preparation, this problem will test algebraic skills and problem-solving abilities. Join us as we break down the steps to solve this challenging equation, offering tips and tricks along the way.

Whether you're a student preparing for a math competition or a math enthusiast looking for a fun challenge, this video is for you. Don't forget to like, share, and subscribe for more math challenges and solutions. Let's dive into this radical equation together!

We'll cover:

Key concepts and definitions
Common pitfalls and how to avoid them
Detailed example problems with solutions
Tips and tricks to solve these equations efficiently

Additional links:

00:00 Introduction
00:21 Substitution
03:45 Solving cubic equation
05:42 Synthetic division
06:25 Quadratic formula
11:02 Discriminant
11:40 Solutions
12:12 Verification

Additional Resources:


#algebrachallenge #radicalequations #mathproblems #mathchallenge #problemsolving #algebra #education #mathematics #matholympiad

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[kprdqvg]

The equation simplifies to 2x^6 -15x^4 -14x^3 +75x^2 -76 =0. By inspection, x=-1 is a solution. [2x^6 -15x^4 -14x^3 +75x^2 -76]/(x+1) = 2x^5-2x^4-13x^3-x^2+76x-76. Again, 2x^5-2x^4-13x^3-x^2+76x-76=0 has x=2 as a solution. These are the two valid solutions.

[TrinityRed]

(x² + y²) * x = 5x and (x² + y²) * y = 5y So xy(y+x) + 7 = 5(x+y) and (x+y)² = x² + y² + 2xy So you get (x+y) and xy faster

[SidneiMV]

7 - x³ = u³
5 - x² = u²

x³ + u³ = 7
x² + u² = 5

(x + u)(x² + u² - ux) = 7
(x + u)(5 - ux) = 7

x + u = 1
xu = -2

t² - t - 2 = 0
(t + 1)(t - 2) = 0

*x = -1* => u = 2
*x = 2* => u = -1

I think there are other roots. Maybe.

[nyjfist]

Θετω 7-χ^3=y^3 αρα χ^3+y^3=7 και χ^2+y^2=5 κλπ