Math Olympiad | A Nice Algebra Problem | Find x and y

math olympiad
olympiad math
Math olympiad question
Math olympiad questions
olympiad math problem
algebra olympiad problems
math
maths
algebra
algebra problem
nice algebra problem
a nice algebra problem
math tricks
imo
how to improve maths
how to solve any math problem
Find the value of x and y?
How to solve x+y=2 and xy=1/2

In this video, we'll show you How to Solve Math Olympiad Question A Nice Algebra Problem x+y=2 and xy=1/2 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #mathtricks #maths

[key_board_x]

(x + y)² = x² + 2xy + y² → given: x + y = 2
4 = x² + y² + 2xy → given: xy = 1/2
4 = x² + y² + 1
x² + y² = 3 → given: x + y = 2 → y = 2 - x
x² + (2 - x)² = 3
x² + 4 - 4x + x² = 3
2x² - 4x = - 1
x² - 2x = - 1/2
x² - 2x + 1 = - (1/2) + 1
(x - 1)² = 1/2
x - 1 = ± 1/√2
x - 1 = ± (√2)/2
x = 1 ± (√2)/2

First case: x = 1 + (√2)/2
y = 2 - x
y = 2 - 1 - (√2)/2
y = 1 - (√2)/2


Second case: x = 1 - (√2)/2
y = 2 - x
y = 2 - 1 + (√2)/2
y = 1 + (√2)/2