Solving a Challenging System of Equations | Harvard MIT Math Tournament (HMMT), Q10, 2021 @tibees

Hello all. I am posting this video solving a challenging system of equations from Harvard MIT Math Tournament. HMMT math tournament is full of interesting yet challenging problems. Harvard MIT Math Tournament, do you want to know what it is? Visit @tibees to know more about it. This question was difficult as we needed to analyze three equations and somehow come up with the maximum value of a certain term based on them. This question in HMMT math tournament is relevant to advanced algebra that you are all welcome to try first before watching the video until the end. Come check this problem out and watch the video until the end. Harvard MIT Math Tournament is full of interesting yet challenging questions that I am planning to cover many of them. More to come! Stay tuned!

#harvardmitmathtournament #advancedalgebra #systemofequations

[pkmath]

Hello guys! There was a typo in 8:11. It is square root of 17 and not 7. It was a typo, but the correct answer was presented right after and in the end. Thanks!

[IshaaqNewton]

Came from Tibees’ video. Great job, dude.

[zeninmaki]

This has become one of my favourite math channels. Prof, I hope your channel grows. And yes, your explanation is so well done.

[vrishankpandey]

As a student who just completed grade 8 (going to grade 9) I'm really thankful to you for actually using such accurate ways of explanation. Considering my grade I would have never been able to think how to do such algebraic expressions using such advanced terminology at such a young age. But somehow with putting a decent amount of concentration I could understand how this answer came along to be, and how this long equation's terms formed! I really respect you for making someone like me also on how to get solutions of such advanced equations even!

[math]

this was challenging, the solution was very well explained, great job, thanks for sharing

[SPRINGGREEN]

Really interesting question, explained quickly and clearly there MIT-Harvard questions are mostly based on algebra manipulation. Thanks.

[lavenderlillymi]

Thankyou so much I hope you do More maths Olympiad exams question your explanations really helped me

[mathnerd]

Dang, I your solution much better than the one from HMMT. you are the best

[apratimtewari]

I could not have thought of the solution just by reading the question, but now I understood it.

You earned a subscription from me sir.

[ieimagine]

K=1 works for the fourth degree polynomial

K=4, I do not seem to make it work, just could not spot the silly mistake at this moment🥴

Thanks for video!

[Min-cvnt]

another best video, thanks for sharing

[UzziWallendorf]

100ab+100ab²+1000ab³->1/3, k =⅛-1-/¹=5 1 -1 ¹ ->1000+100+42+97-45->5272

[lumbradaconsulting]

Although does not affect the final result. Your values for x, y, z are still a mistery for me. There are the values I found while solving the problem. x = 2/(1+SQRT(17)) y= 4/(5+SQRT(17)) z= 8/(-1+SQRT(17)).

[BRUBRUETNONO]

To go further, it would be interesting to solve (and to explain how to do it) completely for the values of x, y and z.
I tried two ways with Wolfram alpha: -first by asking to solve thé initial system and it gave complex values,
-second, i asked to solve by replacing xyz with the value (5+sqrt(17))/2 and (5-sqrt(17))/2 and 1 and 4;
Then according the différent solutions for xyz, the value 1 gives no solution as xyz<>0, the value 4 gives x=-1, y=2, z=-2, the values (5+/-sqrt(17))/2 give only real solutions using sqrt(17) and integers in fractions for x, y, z.
Maybe someone can explain thé différence in Wolfram alpha results and confirm the good results !
Thanks in avance and thanks for the quality exercises !
Greetings !

[justinmanzo]

At 10:17 what formula do you use? How do you know a, b c, and d are equal to that? Where are you getting b from?

[jmsamia]

Please solve this Differentual Equation in the next video. I have a little problem with this equation.

x + y = 9, x – y = 6 and p = 2a – 7b + 4c, Q = –7b – 3a + 7c

(1) Determine the value of p² – PQ + Q². When a = 2, b = 1, c = 3

(2) Show that 2x² + 2y² + 7xy = 783 ÷ 4

J M SAMIA
Grade VI(6)
Nabarun Public school
Sherpur-2100

[domedebali]

Your explanation is just the best, once your video is in viral, you will have a million subs.

[wjqbquy]

+1

Put xyz=w

(y+1)(z+1)(x+1)=
w+(x+y+z)+(xy+yz+xz)+1

Re arrenge equation
x(y+1)=1-xyz
y(z+1)=2-xyz
z(x+1)=4-xyz
Multy these eqs becomes

w(y+1)(z+1)(x+1)=(1-2w) (2-w)(4-w)

w(w+x+y+z+xy+yz+xz+1)
=(1-w)(2-w)(4-w)

But x+y+z+xy+yz+xz=
1-w+2-w+4-w by add 3 eq

w(w+1-w+2-w+4-w+1)
=(1-w)(2-w)(4-w)

2(4-w)=(1-w)(2-w)(4-w)

Either w=4, ignore
OR
2w=(w-2)(w-1) then
w=0.5(5+sqr17)

I think its easer do you agree with me profissor

[ritsu]

When you get 5 how do you know that a = 5 and b = 1 it can be the inverse ?

[GuidoSalami]

i dont get at 2:33, where does 3-k come from