Hi Sybermath. I really enjoy your videos. I want to know if there is a similar method to solve if, 11a+ ab + 11b = 6436 or 11(a+b) + ab = 6436?. a and b are postive integers. Or generally, c(a+b) + ab = x, where c and x are known. Other than adding a perfect square to both sides and factorizing, and then doing trial and error method. Would be grateful if you can answer this.
I'm not sure if there's another way to do it. After factoring, it's not guess and check, though. We are looking for factors of a number which can be found just by writing different ways the number can be factored. Looking at the prime factors will also help. Suppose we have 24. We can do the following: 1x24, 2x12, 3x8, and 4x6 OR 24 = 2^3*3^1 The factors are 2^0, 2^1, 2^2, 2^3 3*2^0, 3*2^1, 3*2^2, 3*2^3 or we can form a sum of the factors using (1+3)(1+2+2^2+2^3) When you distribute, you'll get a sum of all the factors...(another formula for finding sum of factors) I hope this helps. Any other ideas?
On Friday I asked my math students “What are the factors of 52?” Silence… OMG! So I asked them how many suits there are in a deck of cards? They quickly answered: “spades, hearts, clubs, diamonds.” So I said, “Right, so that’s 4 suits. Now what’s 52 divided by 4.” SILENCE… what could these kids have been doing from Kindergarten to the end of 6th (or 7th) grade to be this terrible at arithmetic!?!? THANK YOU!!! (At least SOMEONE is still doing mathematics.)
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Awesome...learned new thing today... I enjoyed it...👍🏻
Great 👍
Simon's Favorite Factoring Trick. 53 is prime with factors 1, 53 and -1, -53. Resulting in (0, 52), (52, 0) and (-2, -54), (-54, -2).
You are fun. Nice problems.
Thanks! 😃
Hi Sybermath. I really enjoy your videos. I want to know if there is a similar method to solve if, 11a+ ab + 11b = 6436 or 11(a+b) + ab = 6436?. a and b are postive integers. Or generally,
c(a+b) + ab = x, where c and x are known. Other than adding a perfect square to both sides and factorizing, and then doing trial and error method.
Would be grateful if you can answer this.
I'm not sure if there's another way to do it. After factoring, it's not guess and check, though. We are looking for factors of a number which can be found just by writing different ways the number can be factored. Looking at the prime factors will also help. Suppose we have 24. We can do the following:
1x24, 2x12, 3x8, and 4x6 OR
24 = 2^3*3^1
The factors are
2^0, 2^1, 2^2, 2^3
3*2^0, 3*2^1, 3*2^2, 3*2^3
or we can form a sum of the factors using
(1+3)(1+2+2^2+2^3)
When you distribute, you'll get a sum of all the factors...(another formula for finding sum of factors)
I hope this helps.
Any other ideas?
Yes it does make sens! ☺
No! cents 😜
Nice!
Thank you! Cheers!
Good videos
Glad you like them!
Nice and eaaasssyyy
Thanks a lot 😊
which app do you use to write?
Notability
is it only available on Tabs?@@SyberMath
a+b=52 or -56
Answer: 52
a=0,b=52 and a=52,b=0 are solutions
a+b=S,...risulta S^2+4S-208 un quadrato perfetto ,..S=52...S=-56
a+b=52
Special trick called s FFT, I was scared at this moment
ooops. sorry 😜
Two methods basically the same. Factoring 53.
kind of
On Friday I asked my math students “What are the factors of 52?” Silence…
OMG!
So I asked them how many suits there are in a deck of cards? They quickly answered: “spades, hearts, clubs, diamonds.” So I said, “Right, so that’s 4 suits. Now what’s 52 divided by 4.”
SILENCE…
what could these kids have been doing from Kindergarten to the end of 6th (or 7th) grade to be this terrible at arithmetic!?!?
THANK YOU!!!
(At least SOMEONE is still doing mathematics.)
First like!
🏆😊
Again!!!!!!!!! a(1+b)+(1+b)=53 -prime.
😁
too easy
If a and b are to be integers (strictly), then only a + b = -54 is the only legal answer.
We know zero is not an integer.
Zero is defined to be an integer.