I proceeded as in method 2 but in a slightly different way. Adding the two equations gave me (a+d)(b+c)=11 and subtracting gave me (a-d)(b-c)=1 The second factorization gives: a-d=1 and b-c=1 or a-d=-1 and b-c=-1 thus a=1+d b=1+c or a=-1+d b=-1+c. substituting into the first factorization gives two equations (1+2d)(1+2c)=11 and (-1+2d)(-1+2c)=11. Factors for 11 are [11,1] [1,11] [-11,-1] [-1,-11] so each of the these two equations gives four answers for c and d from which a and b can be calculated using either a=1+d b=1+c or a=-1+d b=-1+c. In total we have 8 solutions sets (a,b,c,d) as follows (6,1,0,5) (1,6,5,0) (-5,0,-1,-6) (0,-5,-6,-1) and (5,0,1,6) (0,5,6,1) (-6,-1,0,-5) (-1,-6,-5,0). Finally I think the formulas for c and d given in the first method are off. For example a=6 b=1 c=0 d=5 is a solution. Method 1 gives c=(6a-5b)/(a^2 - b^2)=(6*6 -5*1)/(36 -1) = 31/35.
@@SyberMath Could you credit the music? There may be others like me who would want to know. I could suggest other music if your voice needs a rest in future videos. I so appreciate your UA-cam channels.
Yes, I think I actually heard something about that! Let us all hope for the soon return of the most beautiful voice on the internet, who indeed NOT speaks too much, but in excellent simplified American English, which is easy to follow!
Syber did a problem in which f(f(x)) =x^2 -x + 1. We were to find f(0). Syber did not find f(x) to solve the problem, but how does one find f(x)? The order of the composite is the square of the order of the original function. But if the order of the composite is not a perfect square, how do we find f(x) as in the above example? This seems like an easy problem but I cannot find f(x). If it is worthy can Syber do a video showing how to find f(x) ?
He lost his voice from being sick so no talking. And I'm sorry if you don't like bluesy jam music. Given that him speaking might not be possible, what audio would you prefer? Telling us that would be a positive statement and constructive. And being positive and constructive gets one a long way in life.
I proceeded as in method 2 but in a slightly different way. Adding the two equations gave me (a+d)(b+c)=11 and subtracting gave me (a-d)(b-c)=1
The second factorization gives: a-d=1 and b-c=1 or a-d=-1 and b-c=-1 thus a=1+d b=1+c or a=-1+d b=-1+c. substituting into the first factorization
gives two equations (1+2d)(1+2c)=11 and (-1+2d)(-1+2c)=11. Factors for 11 are [11,1] [1,11] [-11,-1] [-1,-11] so each of the these two equations
gives four answers for c and d from which a and b can be calculated using either a=1+d b=1+c or a=-1+d b=-1+c. In total we have 8 solutions sets
(a,b,c,d) as follows (6,1,0,5) (1,6,5,0) (-5,0,-1,-6) (0,-5,-6,-1) and (5,0,1,6) (0,5,6,1) (-6,-1,0,-5) (-1,-6,-5,0). Finally I think the formulas for c and d given
in the first method are off. For example a=6 b=1 c=0 d=5 is a solution. Method 1 gives c=(6a-5b)/(a^2 - b^2)=(6*6 -5*1)/(36 -1) = 31/35.
Speedy recovery!
Thumbs up for bluesy jam music. Maybe change up the audio on different videos? (And wishing your voice comes back "2u".)
Thanks
@@SyberMath
Could you credit the music? There may be others like me who would want to know.
I could suggest other music if your voice needs a rest in future videos.
I so appreciate your UA-cam channels.
Why are you not speaking ? I personally liked the "only voice with no bgm" vibe in your videos 😅
I believe he has lost his voice due to illness.
Yes, I think I actually heard something about that! Let us all hope for the soon return of the most beautiful voice on the internet, who indeed NOT speaks too much, but in excellent simplified American English, which is easy to follow!
@@christianandersson7416 Thank you for the kind words! 🥰
😂😂😂
There is a problem, I think the correct answer is A=6, B=1, C=0, D=5...what do you think. ;-)
Voice>>>>
Finally back 😄
In the second method, I see that the letters are in a different order than originally written.
It's symmetrical. It's the same problem wither way.
Syber did a problem in which f(f(x)) =x^2 -x + 1. We were to find f(0). Syber did not find f(x) to solve the problem, but how does one find f(x)? The order of the composite is the square of the order of the original function. But if the order of the composite is not a perfect square, how do we find f(x) as in the above example? This seems like an easy problem but I cannot find f(x). If it is worthy can Syber do a video showing how to find f(x) ?
Odd that you are commenting on this video about another video. Not bad, just odd.
well that was unexpected
Answers may be 1,6,5,0 or 0,5,6,1 in order.
There are 4 variables, but only 2 equations.
Diophantine Equation
easy, peasy! the music is amazing...
No.
Thumbs-down on the video for you not speaking and also for that music playing.
He lost his voice from being sick so no talking. And I'm sorry if you don't like bluesy jam music. Given that him speaking might not be possible, what audio would you prefer?
Telling us that would be a positive statement and constructive. And being positive and constructive gets one a long way in life.
Thanks Qermaq for clarification 😊