A Nice Rational Equation | 99% Failed to Solve | Algebra Challenge

A Nice Rational Equation | 99% Failed to Solve | Algebra Challenge

Welcome to another rational equation challenge! In this video, we tackle a nice rational equation using the powerful method of substitution. This problem is perfect for sharpening your algebra skills and preparing for competitive math exams.

Watch as we break down the steps to solve this equation, providing clear explanations and tips along the way. Whether you're a math enthusiast or a student aiming to excel in Olympiad competitions, this video will help you understand and master rational equations.

Don't forget to like, comment, and subscribe for more math challenges and solutions. Happy solving!

In this tutorial, you'll learn:

1- Fundamental concepts and definitions of rational equations
2- Step-by-step method of substitution to solve rational equation
3- Common pitfalls and how to avoid them
4- Expert tips and tricks for solving problems quickly and accurately
5- Practice problems with detailed solutions

Additional Resources:

#matholympiad #rationalequations #mathtutorial #substitution #math #mathskills #learnmath #education #algebra #matholympiadpreparation

Join us as we unlock the secrets to excelling in rational equations and take your Math Olympiad prep to the next level. Don't forget to like, subscribe, and hit the bell icon for more Math Olympiad videos. Let's conquer those equations together!

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[tejpalsingh]

Moving 2nd term to other side n simplify with substitution. Gives.
X = + -√21+5 ; (-9+ -√65)/2

[Shobhamaths]

If u take lcm and simplify
x^4-x^3-82x^2-4x+16=0
Divide with x^2 then
x^2+16-(x+4/x) -82=0
Let t=x+4/x
t^2-t-90=0
t=10, -9
x=(-9±√65) /2, 5±√21👍

[kassuskassus]

We have to solve x^4-x^3-82x^2-4x+16=0. Divide both sides by x^2 and let a=x+4/x and solve for a the equation a^2-a-90=0. We'll get a=-9 and then x=(-9+or-sqrt65)/2 and a=10 that gives x=5+or-sqrt21

[RashmiRay-cy]

The equation simplifies to x^4-x^3-82x^2-4x+16=0 > x^2+16/x^2 -(x+4/x) =82 > (x+4/x)2 -(x+4/x) -90=0 > x+4/x=-9, 10. If x+4/x=-9, x=1/2[-9+/-√(65)]. If x+4/x=10, x=5 +/-√(21).

[허공]

x^4 - x^3 - 82x^ 2 - 4x + 16 = 0
let x = 2t and dividing 8t^2 => 2t^2 - t - 41 - 1/t - 2/t^2 = 2(t^2 + 1/t^2) - (t + 1/t) - 41 = 0
let u = t + 1/t => 2(u^2 - 2) - u - 41 = 2u^2 - u - 45 = (u - 5)(2u + 9) = 0
=> u = {5, -9/2} => t = { (5±√21)/2, (-9±√65)/2 } => x = { (5±√21), (-9±√65) }

[RyanLewis-Johnson-wqxs]

(5x-4)/(x^2)+(70)/(x+2)^2=1 x=5±Sqrt[21] It’s in my head.

[潘博宇-kl]

X=5+(21)^(1/2), 5-(21)^(1/2), [-9+(65)^(1/2)]/2, [-9-(65)^(1/2)]/2

[RealQinnMalloryu]

(5x)^2 ➖ (4)^2/(x^2)^2+{70x+70x ➖ }/2x^2 ={25x^2 ➖ =74.1xx^3 2^37.1x^3 2^37^1.1x^3 2^1^1.1x^3 2.x^3 (x ➖ 3x+2).