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- เผยแพร่เมื่อ 18 ต.ค. 2024
- A Nice System of Equations | Math Olympiad | Algebra
Welcome to infyGyan, as we tackle an interesting system of equations from the Math Olympiad! In this video, we will break down the steps needed to solve this challenging problem and provide you with tips and strategies to tackle similar questions. Whether you're preparing for a math competition or simply love solving algebraic puzzles, this video is for you. Don't forget to like, comment, and subscribe for more engaging math content!
Topics Covered:
System of equations
Algebra
Problem solving
Algebraic identities
Algebraic manipulations
Solving systems of equations
Factorization
Quadratic equations
Math tutorial
Math Olympiad
Math Olympiad Preparation
#mathtutorial #systemofequations #problemsolving #mathhelp #algebra #learnmath #education #mathskills #math #matholympiad
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![เปิดใจ "อาจารย์เบียร์ คนตื่นธรรม" อดีตเคยสุดทุกทาง ถ้าใช้หนี้หมดไปบวชแน่ l [Nickynachat]](http://i.ytimg.com/vi/IxeE0xVhy08/mqdefault.jpg)
Nice.
It was unnecessary to restrict yourself to real numbers. It came from the solution.
Another way is to cube the second equation: x³ - y³ - 3xy (x - y) = -27 and replace x - y with -3: x³ - y³ = -9 xy - 27 and use this result to substitute x³ - y³ in the first eq.
(x;y)= (-2;1); ( -1; 2);
{(-3+ -√5)/2; ( 3+ -√5)/2}
Let xy=p and solve for p the equation 9p^2+27p+18=0. We'll get p=-2 and p=-1, so xy =-2 and xy=-1. x-y=-3 and xy=-2 gives (x,y)=(-2,1); (-1,2). x-y=-3 and xy=-1 gives (x,y)=((-3+sqrt5)/2; (3-sqrt5)/2); ((-3-sqrt5)/2, (3+sqrt5)/2).
(y ➖ 3x+2). ➖ 3^1 (y ➖ 3x+1) .
X=-1,-2,((-3+√5)/2), ((-3-√5)/2)
If xy = t, the equations yield t[x^2+y^2+t] =-6 > t[(-3)^2+3t]=-6 > t^2+3t+2=0 > t= -1,-2. If t=-1, y=-1/x > x+1/x=-3 > x = 1/2[-3 +/-√5], y = 1/2[3+/1√5]. If t = -2, x+2/x=-3 > x=-1,-2, y=2,1.
х^3-у^3=(х-у)*((х-у)*2-3ху)
Если ху=а
а*(3-а)=-2
а=-1, а=-2
Ну и х-у=-3, ху=-2 или ху=-1
Решение не составляет труда