Find Two Numbers Whose Sum is 55 and Whose Product is 684

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Find Two Numbers Whose Sum is 55 and Whose Product is 684

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what in tarnation lol. why did you do all the algebra just to guess the numbers at the end? you could've just done that at the beginning LOL. factoring your quadratic equation is equivalent to solving the problem :)

persistenthomology

Correct me if I'm wrong, but if you can do the step you did at around 2:20, you can solve the problem in the first place!

shadowrottweiler

you did all that just to solve the quadratic by guessing numbers that add to 55 and multiply to 684. Exactly the problem we are presented with in the beginning. I know you could use the quadratic formula but we came all that way just to loop back to essentially the original problem and approach it with a guess.

justinbishop

I think after you’ve got your quadratic equation, it would have been better to use the quadratic formula instead of guessing the two numbers.

I think this is especially better when teaching students as they’re not going to be able to guess that the solutions are x = 19 and x = 36

lilbowwowy

Hey Man! Love the videos, got into math beacouse of you!

Briggzy_Gibzy

What about a diffrent way to solve the problem? 6+8+4=18, 55-18= 37.
18×37=666, not the correct answer, but close.Therefore, if you take 684÷19= 36.And 19+36=55.
To check it, 684÷38=18,
18+38=56.
How about that one?

charlottepeukert

You could use x or y = (sum±√sum^2-4*product)/2

fdfsfc

Use the fact that 4*a*b = (b + a)^2 - (b - a)^2. Deduce that b - a must equal 17. Then we have that b + a = 55, b - a = 17. So 2*b = 72 and 2*a = 38.

slipstream

Hi, Math Sorcerer...
I've been enjoying your videos, I too love old books (math or otherwise) and just using pen and paper (and white out)
...AND I love your old TI-84 Silver Edition! I too have a collection of older calculators...
(Though my favorite new calculator these days is the TI-36X Pro)

But this video was a bit anti-climatic! However...

I'll tell you how _I_ "guess" the two numbers (whether a solution to a quadratic or not):
If we're not going to complete the square or use the quadratic formula, then I make a list of integral factor pairs of 684:
1 x 684
2 x 342
3 x 228
4 x 171
6 x 114
9 x 76
12 x 57
18 x 38
19 x 36 ...
All the while taking the sum... and Bingo, the last one was the pair, so I stop!
There's a bit more to it when the leading coefficient of x^2 is not 1.

michaelkrupa

hiii sir I from India and your video are useful

Saurav.

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