Can You Simplify This Expression? | A Nice Algebra Challenge | IMO

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Can You Simplify This Expression? | A Nice Algebra Challenge | IMO
Think you have what it takes to simplify this algebraic expression? Join us in this exciting Algebra Challenge inspired by the International Mathematical Olympiad (IMO). We'll walk you through the steps to simplify complex algebraic expressions, providing useful tips and techniques along the way. Perfect for students preparing for math competitions or anyone looking to sharpen their algebra skills.
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Topics covered:
Algebra Challenge
Simplification
Simplify Expression
Expressions
How to simplify expressions?
Math Olympiad
Algebra
System of equations
Math Tricks
Algebraic identities
Algebraic manipulations
Algebraic Challenging Problem
Math Olympiad
IMO
Math Olympiad Preparation
Math Tutorial
Algebra Challenge
Substitution
Math skills
#algebrachallenge #matholympiad #imo #mathematics #algebra #problemsolving #mathcompetition #mathskills #learnmaths
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Опубликовано:

20 июн 2024

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Комментарии : 10

@user-ji5su2uq9m Месяц назад

from 4:05 , we can easily solve the problem without calculating ab. a + b = -1, a + 6 = b^2 --(1) b + 6 = a^2 --(2) => (1) + (2) => a^2 + b^2 = (a + b) + 12 x^2 + y^2 = (a + 2)^2 + (b + 2)^2 = a^2 + b^2 + 4(a + b) + 8 = (a + b) + 12 + 4(a + b) + 8 = 5(a + b) + 20 = 5*(-1) + 20 = 15

@mohammedsaysrashid3587 Месяц назад

It was a wonderful introduction and clearly explaining.. thanks, Sir 🙏....finally x^2 +y^2 =15 ...

@SidneiMV Месяц назад

x + 4 = (y - 2)² y + 4 = (x - 2)² x + 4 = y² - 4y + 4 y + 4 = x² - 4x + 4 x = y² - 4y y = x² - 4x x² + y² = 5(x + y) x² - y² - 4(x - y) = - (x - y) x² - y² = 3(x - y) x + y = 3 x² + y² = 5(x + y) x² + y² = 15

@backgammonmaster Месяц назад

Dear sir ,this can be solved in MUCH easier way. First expand and simplify both givens . Call them * and #. now first subtract and simplify result x+y=3 . now go back and multiply and simplify * and # you get xy=-3 The rest is obvious. takes 2 min MAX 🙂. Thanks

@user-ny6jf9is3t Месяц назад

Χ^2+y^2=0, ή =15, ή=50

@RajeshKumar-wu7ox Месяц назад

3,18

@user-nd7th3hy4l Месяц назад

X^2+Y^2=20

@tejpalsingh366 Месяц назад

0; 50;15

@davidshen5916 4 дня назад

1️⃣-2️⃣ X-Y=（X+Y-4）（Y-X），（X-Y）（X+Y-3）=0， X！=Y，因此X+Y-3=0， 1️⃣➕2️⃣， X+Y+8=X^2-4X+4+Y^2-4Y+4， X^2+Y^2=5（X+Y）=5*3=15

@johnstanley5692 16 дней назад

Easier? g1=x+4-(y-2)^2 (= 0), g2=y+4-(x-2)^2 (=0), g3=x^2+y^2 (=?). 1st step g2/g1 -> p1= - y^4 + 8*y^3 - 12*y^2 - 15*y (=0) 2nd step g3/g1 -> p2= y^4 - 8*y^3 + 17*y^2 (=?). 3rd step p2/p1 -> p3 = 5*y^2 - 15*y (= x^2+y^2). Now solve p1 to obtain values, 'y' p1= -y*(y-5)*(y^2-3*y-3) => y={ 0, 5, 3/2 - 21^(1/2)/2, 21^(1/2)/2 + 3/2} . Subs y into p3 =>x^2+y^2 = {0, 50, 15, 15}