Olympiad exam sample papers | A great math challenge

Solve for x,y - integers.
If you're reading this ❤️. What do you think about this problem?
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[@foogod4237]

*This is wrong.*
Clearly, x² = 9 and y² = 2000. Therefore, x = 3 and y = 20√5, so *x + y = 3 + 20√5 ≅ 47.721*
Or maybe x = 7 and y = -14√10, so *x + y = 7 - 14√10 ≅ -37.271*
In fact, this question has *an infinite number of possible answers.* This should actually be obvious, because you've got *only one equation with two variables* to work with. There is simply not enough information to solve this problem.
Just figuring out one number and writing it down as "the" answer *is wrong.* This problem actually *has no defined solution* as it is stated.

[@purplebrain-complementsvid4173]

exactly what i was wandering: why should the answer be part of N? and why does he even get rid of the negative solutions so easily?

[@rorydaulton6858]

Two comments:
1) I see that you put the restriction of x and y being integers in your description to the video. It would be better if you also put that at the start of the video, both in the opening picture and in your spoken words. Putting that in the thumbnail would also help. Since you only look at positive solutions, it would be even better to say x and y are positive integers.
2) You never explain why x and y must be multiples of 7--it is very possible for two non-multiples of 7 to add to a multiple of 7² = 29. But it can be easily shown that x and y are multiples of 7. If you look at the multiples of the square numbers modulo 7 (the remainders after division by 7) you quickly see that the only possibilities are 0, 1, 2, and 4. The only way to add two of those and get a sum divisible by 7 is 0 and 0. Thus x² and y² are equal to 0 modulo 7, hence x² and y² are multiples of 7, hence x and y are multiples of 7. You really should give some such reasoning in the video.

[@onkotonkoblu]

FOR EVERY PUSH UP THIS LIKE GETS I WILL DO A COMMENT

[@thegiganerd395]

What?

[@Fire_Axus]

it is sqrt(2xy+9)

[@ScientistPrepper]

creative.

[@Ordinal_Yoda]

AB = 5, BC = 678
A=?,B=?,C=?

[@empathy1234]

You got 2 equations but 3 variables. Therefore, you'll have infinite # of solutions.

[@Ordinal_Yoda]

@@empathy1234 Thanks. No wonder it's been taking so long.