√81 = 8+1. What About 4-Digit Numbers?
HTML-код
- Опубликовано: 19 апр 2024
- My previous video explaining √81 = 8+1: • Is 81 the ONLY Two-Dig...
My video on √81 = 8+1 went viral, and viewers pointed out that finding two-digit numbers are too easy that it can be done by bashing (testing every perfect squares), urging me to expand the problem with more digits. So here I present you how to find all 4-digit numbers xyzw satisfying the relation √(xyzw) = xy + zw. Since the RHS consists of only 2 numbers, we can use the same quadratic equation method used in my previous video.
#NumberTheory #DiophantineEquations #IntegerRoot
------------------------------------------------------------------------------------
CORNERSTONES OF MATH features quality math problems to strengthen your math fundamentals and problem-solving ability. Problems are generally on high school level (with some deviations), spanning over topics such as algebra, discrete mathematics, calculus, geometry, statistics, trigonometry, etc. I hope that this channel provides some intellectual pleasure and make you appreciate the beauty of math itself.
Please consider giving a Like to this video and Subscribing to my channel, it really means a lot for the creator like me, and you will be introduced to many more interesting math videos!
494 + 209 = sqrt(494209)
2450+2500 = sqrt(24502500)
2550+2500 = sqrt(25502500)
5288+1984 = sqrt(52881984)
6048+1729 = sqrt(60481729)
Python says hi.
Hi. Although my channel focuses on understanding mathematical principles and logic rather than utilizing programming languages, I do understand the importance of programming and I appreciate the examples given for higher number of digits.
Wow❤
Wow indeed. ❤
In desmos, I graphed \sqrt{10x+y} = x+y, it gave solutions and when y is a whole, it gave 8,1. 0,1 is a answer but doesn't satisfy x≠0
If you only seek for answers, that would work (although if number of digits becomes large it would be very difficult to identify integer-coordinate points with only eyeballs). I attempted to provide a solution that allows us to apply and review some basic mathematical theories (quadratic equation and properties of integers), which can be applied to other problems of similar type (for example, finding the integer roots of the multivariable quadratic equation).
sqrt(2025)=20+25
I wonder what method you used to find that one. Anyway, please go check my video for more answers!
@@CornerstonesOfMath it's a bit underwhelming 😅 I just guessed and checked on desmos, although there has to be a more elegant way to find it