I can confirm your answer, at least, assuming I didn't make any mistakes. My method was simple: (spoilers) (spoilers) (spoilers) first, re-arrange the stuff in the original equation to solve for floor(x). Then we have the equations floor(x) = k when k 10, because you're multiplying by a negative number. (I also tested whether x=10 could be a solution to the original problem, just to make sure I didn't miss anything) From there you can factor the inequalities to narrow it down to 4 possible values for "k." Then you go back to the original equation and solve it four times, once for each possible value of "k." This will yield exactly 3 solutions, the ones that you listed above.
What sorcery is this? Today i changed my phone from dark mode to white mode after an year or so and just today you are premiering a video not in dark mode!
Floors and ceilings make me dizzy. Are there other architecturally-named functions? How about the Wall-is product? :D Either my water heater is out of Euler it was broken by the radicals in the basement. I should use a quintic equation to protect the water heater as it can't be solved by radicals.
I solved this divided by cases that x is/isn't an integer. (i)if x is an integer, x/(x+4)＝(5floor(x)－7)/(7floor(x)－5) ⇔x/(x+4)＝(5x－7)/(7x－5) ⇔(x－2)(x－7)＝0 and x≠－4 ⇔x＝2，7 (ii)if x is NOT an integer, Let floor(x)＝t（t∈Z） and x＝t+a（a∈R，0
Hey SyberMath, I've been enjoying your videos for some time and recently I've hit a sort of ceiling on my problem solving skills. I'm understanding less and less of what I ought to do in problems you present. What sort of practice do you recommend to tackle these problems? I hope to hear from you soon.
Good question. I would just keep practicing using different resources and make problem solving a habit while enjoying the experience. Try to solve a problem in different ways. If you don't have ideas, read the solutions, and then without looking try to reproduce the solution on a piece of paper. Sometimes reading part of the solution and then trying to fill in the blanks helps. Do not lose hope as good problem solving skills are gained over time and with plenty of practice. If you need the basics, use a good textbook depending on what you need: Algebra, Number Theory, etc. Math competitions are good resources for non-routine, non-standard problems. You can check out older videos of mine, too (Ad break! 😂). Always be curious and ask questions! Good luck on this journey and remember it's the journey that matters, not the destination! 😉😊 I hope this helps p.s. quick suggestion: Your English is fine. Consider changing your UA-cam name. 🙃
Usually I'd edit my comment,but since my heart would be gone if I'd edited it,so here are some memes Graphs on Sybermaths videos be like:AMOGUS (because Amogus gets everywhere) Sybermath:Everywhere I go I see his face.
I'm from Czech Republic 🙋♂️🇨🇿
Good to see you, Adam! 😊
I've watched so many videos of yours on floor fnc that solving this particular problem is not a problem for me anymore.
Nice!
@@SyberMath you're the best channel growing
I got three solutions to the problem:
1). x = 2
2). x = 46/7
3). x = 7
btw that's all solutions of this equation
I can confirm your answer, at least, assuming I didn't make any mistakes. My method was simple:
(spoilers)
(spoilers)
(spoilers)
first, re-arrange the stuff in the original equation to solve for floor(x). Then we have the equations floor(x) = k when k 10, because you're multiplying by a negative number. (I also tested whether x=10 could be a solution to the original problem, just to make sure I didn't miss anything)
From there you can factor the inequalities to narrow it down to 4 possible values for "k."
Then you go back to the original equation and solve it four times, once for each possible value of "k." This will yield exactly 3 solutions, the ones that you listed above.
At 7:27, -1 is not a root, but a vertical asymptote. The graph that was drawn is wrong, as the function can only cross the axis twice (at x=2, x=7).
That's not a graph. It shows that the sign changes at x=-1
Ooh white background? Interesting, reminds me of my old videos
😁
Splendid and can't wait. great content bro!
Appreciate it!
What sorcery is this?
Today i changed my phone from dark mode to white mode after an year or so and just today you are premiering a video not in dark mode!
Lol 🤭🤭
😁
Floors and ceilings make me dizzy. Are there other architecturally-named functions? How about the Wall-is product? :D
Either my water heater is out of Euler it was broken by the radicals in the basement. I should use a quintic equation to protect the water heater as it can't be solved by radicals.
Haha, nice one! 😁😁😁
I solved this divided by cases that x is/isn't an integer.
(i)if x is an integer,
x/(x+4)＝(5floor(x)－7)/(7floor(x)－5)
⇔x/(x+4)＝(5x－7)/(7x－5)
⇔(x－2)(x－7)＝0 and x≠－4
⇔x＝2，7
(ii)if x is NOT an integer,
Let floor(x)＝t（t∈Z） and x＝t+a（a∈R，0
Good thinking
Very interesting and clever approach :)
For some reason i struggle with the inequality method.
I rewrote x=n+a , 0
Wow nice solution
Hey SyberMath,
I've been enjoying your videos for some time and recently I've hit a sort of ceiling on my problem solving skills. I'm understanding less and less of what I ought to do in problems you present. What sort of practice do you recommend to tackle these problems? I hope to hear from you soon.
Good question. I would just keep practicing using different resources and make problem solving a habit while enjoying the experience. Try to solve a problem in different ways. If you don't have ideas, read the solutions, and then without looking try to reproduce the solution on a piece of paper. Sometimes reading part of the solution and then trying to fill in the blanks helps. Do not lose hope as good problem solving skills are gained over time and with plenty of practice. If you need the basics, use a good textbook depending on what you need: Algebra, Number Theory, etc. Math competitions are good resources for non-routine, non-standard problems. You can check out older videos of mine, too (Ad break! 😂). Always be curious and ask questions! Good luck on this journey and remember it's the journey that matters, not the destination! 😉😊
I hope this helps
p.s. quick suggestion: Your English is fine. Consider changing your UA-cam name. 🙃
@@SyberMath My goodness! Its probably the largest text you have replied as far i have seen.
I too suggest the same. 😂😂😂
@@ashishpradhan9606 Haha! Thanks, Ashish. Hope to see you at the PREMIERE soon
@@SyberMath Absolutely! 🥰🥰🥰
3:05 It is also interesting that solve n = (-x-14)/(x-10).
Very cool!
What an amazing function (floor) now i am familiar with floor function and i can solve it in majority of the time 😎 thank uuuuuu !!!!!!!!
My pleasure! 💖
x=2,46/7 and 7 are correct options.
Another great explanation, SyberMath!
Glad you think so!
@@SyberMath I got x=2.
i=i
or i²=i²
or (✓-1)²=[(-1)^1/2]²
or -1= [(-1)^2]^1/2
or -1= 1
What do you think ?
absolute values for the win
Genial floor equations. From Catalonia
Many thanks!
Beautiful equation
Thank you
Nice video, but even the range 2
Yes!
@@SyberMath so welcome you are!
Very interesting!
Glad you think so!
We can solve it like
x= I + f
Where I is an integer and f belongs to [0, 1) And then we can manipulate to get the same answer
👍
The fact that {x} lies in between 0 and 1 (0 inclusive) always helps in these kind of problems. x=2, 46/7 and x=7 are the solutions.
But isn't function used there is gif instead fractional part because fractional part belongs to [0,1)
@@kusumjaiswal6404 u can write x as GIF of x + FRAC of x
@@kusumjaiswal6404 Replace [x] with x-{x}, then write {x} in terms of x.
@@arundhatimukherjee yes yes..i forgot to use that property..
Excellent...then what is the final value of x??
What is it? 😉🙃😁🤩😂
Your channel grows fast Cool 💗💗😍🤩😝
Thank you for the support! 💖
Oh my god it's so cool.
Usually I'd edit my comment,but since my heart would be gone if I'd edited it,so here are some memes
Graphs on Sybermaths videos be like:AMOGUS (because Amogus gets everywhere)
Sybermath:Everywhere I go I see his face.
سؤال جميل وكذلك الحل رائع
شكرا جزيلا لك
Nice question. I used your method 👍😁
Great 👍
10 numara anlamışsınız hocam ağzınıza sağlık🤝🤝😁😁
nice question sir thank u
All the best
wow is crazy
Very good
Thanks
U r best on making vedio on floors
So nice of you
@@SyberMath one requested problem plz
√(a)+√(ab)+√(abc)=12
√(b)+√(bc)+√(abc)=21
√(c)+√(ac)+√(abc)=30
Then find a²+b²+c²
I like your channel so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Haha! Thanks, aash!
@@SyberMath you're so welcome!!!!!!!!!!!!!!!!1!!!!!!!!!1
@@SyberMath you are so awesome! & welcome!
sorry for cheating, haha:
Solve[x/(x + 4) == (5 Floor[x] - 7)/(7 Floor[x] - 5), x, Reals]
also try:
Solve[x/(x + 4) == (5 Ceiling[x] - 7)/(7 Ceiling[x] - 5), x, Reals]
😂
0≤{x}
👍
5
👍👍👍👍
😊
may I write my solution here?
Yes. The rules now permit you to put solutions, methods, ideas, and other spoilers into the comments section.
Even before stream?
@@hirokitokuyama Yes.
if you are afraid of n being negative; then you can square both sides first.
I'm scared! 😂
👍❤
💖
@@SyberMath you're the best!!!!!!!!!!!
Huh White background
😁
Please slove this problem (7^x)+2=3^y
Limit X tends to infinity (x) / (x-1)! = ?
How can this be solved?🥺
Isn't it 0?
@@SyberMathI do not understand that! Although or is, but how?
@@pabitradas6362 plug x=10,100,1000 etc and you will found out the limit tends to 0