I Solved a Problem from IMO 1963

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[@erikroberts8307]

You know, I've often wondered how you graded your students on their homeworks, test papers, and quizzes in your classroom. Did they ever get extra points for originality or for showing that there are multiple ways to solve a problem (i.e. 1st method, 2nd method, etc.). But more importantly, did you just give them a score, like 87.5%, or did you give them a score that looked like another mathematical equation for them to figure out? (x = 7/8).

[@ulisses_nicolau_barros]

This is a good question. I used to teach Math in the past, but I gave 0 to 10 score.

[@SyberMath]

Good question! I always encouraged multiple methods and asked them to explain it to me. You’ll be surprised how ingenious they can be

[@pietergeerkens6324]

I substituted p = 4q early on, to cancel out those coefficients and keep the arithmetic easier.

[@SyberMath]

Good thinking!

[@kh_KIM_0542]

6:09 Where's '16p' on the left side in cyan color formula?

[@mikeparfitt8897]

Between the yellow formula at 4:54 and the cyan formula at 5:19 the 16p got dropped. This was noticed at 6:01 and hastily corrected (without proper explanation) which is how the (p+4)^2 term at 6:01 changed into (p-4)^2 by 6:28

[@kh_KIM_0542]

​@@mikeparfitt8897got it. Now I see 16p was not excepted but included.

[@MarieAnne.]

I came looking for this comment as soon as I noticed it was overlooked. Glad to know it gets rectified later.

[@abhialt]

Would have helped to put the actual question at the outset.

[@SyberMath]

Good idea!

[@emanuellandeholm5657]

If x and p are in R with no further restrictions you could have solutions when the Im[] of the sum of the radicals cancel out. Maybe this can't happen in this specific case, but you could certainly craft a similar type problem with looser restrictions on x and p.

[@alextang4688]

This kind of question is somehow related to domin and range of the square root. 🙂🙂🙂🙂🙂🙂

[@yoav613]

Nice!

[@SyberMath]

Thanks!

[@Blaqjaqshellaq]

It might be easier if you substituted with t=x^2.

[@luunguyen193]

you may mistake that x>=0 and x^2>=1 x>=1 is the right condition

[@lucaswarnke3668]

x=1, p=0

[@EatThatLogic]

I solved a problem from IMO 1976 😁