Cracking an Ultimate System of Equations 🌟 | Math Olympiad
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- čas přidán 6. 07. 2024
- Cracking an Ultimate System of Equations 🌟 | Math Olympiad
Discover the ultimate techniques for solving systems of equations and ace the Math Olympiad! 🌟 In this video, we break down complex problems into simple steps, providing you with the tools and strategies you need to succeed. Whether you're a math enthusiast or preparing for a competition, this guide will help you master systems of equations like a pro. Watch now and elevate your math skills to the next level! 🧠✨
Topics covered:
System of equations
Algebra
Substitution
Problem solving
Algebraic identities
Algebraic manipulations
Solving systems of equations
Math enthusiast
Math tutorial
Math Olympiad
Math Olympiad Preparation
Time-stamps:
0:00 Introduction
2:15 Algebraic manipulations
5:20 Solving system of equations
6:56 Algebraic identities
12:05 Solutions
#mathtutorial #systemofequations #problemsolving #mathhelp #algebra #learnmath #mathtricks #studytips #education #solvingequations #mathskills #mathenthusiast #stem #math
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Thanks for watching!
another approach
let a = √x, b = √(x + 32), c = y - 1 then a^2 - b^2 = -32 --- (1)
√x + √(x + 32) = (2 - y)^5 => a + b = - (c - 1)^5 --- (2) since a + b >= 0 , c a - b = (c + 1)^5 --- (3)
(2)*(3) => (a + b)*(a - b) = a^2 - b^2 = -32 = -2^5 = -(c - 1)^5*(c + 1)^5 = -((c - 1)*(c + 1))^5
(c - 1)(c + 1) = c^2 - 1 = 2 => c^2 = 3, since c 2a = - (c - 1)^5 + (c + 1)^5 = 2*(5c^4 + 10c^2 + 1) =2*(5*9 + 10*3 + 1) = 2*76
=> a = 76 => x = 76^2 = 5776 , y = c + 1 = 1 - √3, answer (x, y) = (5776, 1 - √3)
（x,y)=(5776,1-√3)
Thank you for sharing Sir🙏....(x,y) =( 5776,-0,731)
Y=1-√3
（2-y）y=-2，2y-y^2+2=0，y=1+√3，1-√3，2-1-√3≤0 is rejected，so，y=1-√3。