Math Olympiad Problem | Nice System of equations Problem | Math Olympiad Training

In this Math Olympiad problem video, we'll tackle System of equations Problem to help with your Math Olympiad training. Get ready to challenge your math skills!
#exponential
#exponents
#exponentialproblem
#maths
#mathematics

[@nexio5454]

With small numbers like this, you can just list perfect squares under 45 and find by try and error. I solved it in 15 seconds like this :))

[@MrRedEngineer]

I agree. But I don't agree with that mention how fast you solve buddy. Lower your ego and accept his solution.

[@nexio5454]

@@MrRedEngineer I accept his solution and it's definitely the most elegant solution. I didn't mean to show off and I'm sorry if my comment seems like I did.
The problem being presented as an olympiad problem (which it clearly isn't), the goal would be to solve fast hence my solution and my exemple

[@matholympiadonlinesolver]

Thank you

[@Abby-hi4sf]

Always a+b > a-b , so you should not have four cases . I will assign the greater factor to the greater eqn

[@coderhub-tech7942]

Does not apply if b is negative, think again

[@Abby-hi4sf]

@@coderhub-tech7942 Let us not forget that every negative number squared is always positive. All variable a, b, c, are sqared on the question
So the answer is a= +/- 3 , b= +/- 6 and c= +/- 2

[@coderhub-tech7942]

@@Abby-hi4sf true, but you are factoring a²-c² or c²-a² depending on your approach, which can include negative numbers, so your argument doesn't work there

[@Abby-hi4sf]

@@coderhub-tech7942 Whether you are factoring a²-c² or c²-a² , the fact remain that each variable is sqared .ex
a²= (-a)² and (-c)² =c² so
a²-c² = (-a)²-c² = a²-(-c)²

[@coderhub-tech7942]

Tried calculating based off the thumbnail, i got c²-a² = -5 so (c+a)(c-a) = -5, using that and a little brute force, the 4 possible values are c = ±2, a = ±3. From there you get b = ±6 which is the solution

[@matholympiadonlinesolver]

Ok thank you

[@bledlbledlbledl]

the way i went about it was very similar to that. looking at the thumbnail, a² must be 5 more than c². starting from 1 and just squaring a few numbers, it didn't take long to notice that 3² was 5 more then 2². from there, finding b² was just a subtract

[@kiloperson5680]

Might I ask what country are you from?

[@matholympiadonlinesolver]

I'm from cambodia

[@kiloperson5680]

@@matholympiadonlinesolver oh i asked because your pronunciation sounded like french to me haha, weird