Separate 27 into two parts whose product is 92. 

I did it by finding the factors of 92. Much simpler. 92/2 = 46; 46/2 = 23 (prime). Factors are 2, 2, 23. For our problem solution 2x2 = 4. 4x23 = 92. 4 +23 = 27. QED Don't ever make a problem more difficult that it has to be. Solving a quadratic to get this solution is unnecessarily complex.

two equations in two unknowns: eq.1 N.1 + N.2 = 27 * eq.2 N.1 × N.2 = 92 ----------------------------- * how else can you separate the number 27 into 2 parts unless you consider 27 to be a collection of integer digits from 0 to 27? The other alternative to dividing 27 into two parts is '2' and '7' who's product /= 92. ---------------------------- eq.1 N.1 + N.2 = 27 eq.2 N.1 × N.2 = 92 eq.1 N.1 + N.2 = 27 N.1 = 27 - N.2 eq.2 N.1 × N.2 = 92 (27 - N.2)N.2 = 92 27N.2 - N.2^2 = 92 N.2^2 - 27N.2 + 92 = 0 quad equation: (-b +/- sqrt(b^2 - 4ac))/2a here: a = 1 b = -27 c = 92 (-b +/- sqrt(b^2 - 4ac))/2a (27 +/-sqrt((-27)^2-4(1)(92) / 2(1) (27 +/-sqrt(729-368)) / 2 (27 +/sqrt(361))/2 (27 +/-19)/2 rt.1 = (27 +19)/2 = (46)/2 = 23 rt.2 = (27-19)/2 = 8/2 = 4 sub conclude N.2 = 23 or 4 eq.1 N.1 + N.2 = 27 for N.2 = 23 N.1 + 23 = 27 N.1 = 4 for N.2 = 4 N.1 + 4 = 27 N.1 = 23 the two parts of 27 are 4 & 23 verify: eq.1 N.1 + N.2 = 27 eq.2 N.1 × N.2 = 92 eq.1 N.1 + N.2 = 27 4 + 23 =? 27 27 == 27 ✔️✔️✔️ eq.2 N.1 × N.2 = 92 4 × 23 =? 92 92 == 92 ✔️✔️✔️

I started by finding the factors of 92.... 2*2*23

I think in this case, using a quadratic equation for this particular problem is like using a bucket-loader to dig a fence post hole. I set up a table of terms that added up to 27: 1+26 - nope; 2 +25 - nope; 3 + 24-nope; 4+23-bingo! Eight quick steps, one solution. I did assume that it would be a single-digit number, and a double-digit number.

Thanks for this problem. I got it right but think I may have taken too long a path. I approached it by creating two equations: x+y=27 and xy=92. Then I solved the first equation for x (x=27-y), then plugged that into the second equation: y(27-y)=92. Then I set that equal to 0 and used the quadratic formula to solve. It worked, but I worry on an exam I'd never get through all the questions if I solve this way. Among other things, I just didn't quickly see that 23 and 4 would get me what I needed so went though the whole quadratic equation. Thoughts about how to solve faster?

We can still solve it without factorization process. If the two numbers are x and y, we have x + y = 27 and xy = 92. Using the algebraic formulae (x - y)² = (x + b)² - 4 xy = 27² - 4 x 92 = 361 = 19². Therefore, (x - y) = 19. Given x + y = 27 and x - y = 19, our X = ½ (27+19) = 23 and y = ½ (27-19) = 4 .

Well, this much shorter way of doing it I factorised using prime numbers.

Separate, not seperate.

Sorta like mashing potatoes with a steam roller(?)

4&23

23 & 4

Seperate?

I factorized 92 and got 2, 2 and 23. 4+23= 27 so answer found. Admittedly this won't work if the numbers in question are not integers.

Why use quadratics when you can use mental arithmetic? 92/2 = 46, 92/3 = 30ish, 92/4 = 23. QED.

it's Beautiful ❤️ Maths is beautiful 🤩😊

Please correct spelling of separate or use spell check . Thank you

4 and 23

17 minutes to solve something I've just done in 1 minute using an equation? I'm not even going to see how it was done in such a long way.

4x23 just did it in my head

I went off into the weeds because I gave up on factoring. 27±19/2 or 23,4 but it took much longer than it should have. lol

23 and 4

I did quadratic equation and I got +4 and +23.... Didn't factor in the minus to get the negative 27🤔

(x+3x-3) (x+2x-2)

Got it, but as they say in sports it was ugly. ;) Now let's watch how do it the right way.

((x+8x-12) (x+1x-11)

Oh 23 x 4 = 92. That took me less than 30 secs or less. At 2:45 am, cant keep my eyes open.

Algo boost!

The numbers are 4 and 23.

23 and 4. Did this by trial and error.

The numbers 23 and 4

4x23

Over here spelling correctly is needed even in maths classes. If a teacher spelt separate like that especially when being inspected it would be a serious mistake and you might have the lesson classed as inadequate. In fact it fails on unclear wording, separate into two parts? how?

92-27=65. (65+27)=9 2

23 x 4 = 92

I just use the quadratic formula. 😊

With all due respect, I think you could say the same things in one-tenth of the time or even less! More people would watch your videos.

Your approach is overly complicated. As others have noted it's simple to find the prime factors. We can see 92 is even so we can divide by 2. This give us 46, also divisible by 2 so we get 23. 23 is prime so were done. 2*2 = 4, 4*23 =92, 4+23=27

Although I appreciate your posts, they're waaaaay too wordy! You take 10 min to say what can be done in one...

4 and 23