Solving an Interesting Algebra Question | Harvard MIT Math Tournament (HMMT), Q2, 2021

We are solving an interesting algebra question from Harvard-MIT Math Tournament (hmmt) in 2021. @tibees has posted a video about 10 days ago explaining what Harvard MIT Math Tournament (hmmt) is and show you some of the examples, and I posted solutions from questions 7 and 10 from the paper in 2021. Here is the solution for question 2 from 2021, Harvard MIT Math Tournament (hmmt). Interesting algebra question to work on! 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 #exponentialfunction #algebra

[ParthJain.]

Watching you solve these questions so smoothly is so satisfying :)

[MrGLA-zsxt]

you are the best math youtuber. never seen anyone explaining the maths problem in such an easy and outstanding wayyy

[UzziWallendorf]

Ab bb 27a b a²+b²->a =6 ->b=9>6²+9²=117

[amitsrivastava]

a^(a-b)*b^(b-a) = 27/8
Without loss of generality,
let a > b. Thus a - b = k > 0
Thus, ( a/b)^k = (3/2)^3. As a and b are positive integers, this is the only possibility. Thus, a/b = 2/3 and k = 3 and this leads to a = 9 and b = 6 which further gives a^2 + b^2 = 117.

[honestadministrator]

(2/3) ^ 3 = 8/27 = ( a / b) ^ ( b - a)
Hereby
a/2 = b /3 = k
3 = b - a= 3 k - 2k = k
Hereby a^2 + b^2 =( 4+ 9) k^2 = 117

[math]

the solution was very well demonstrated, thanks for sharing

[mathnerd]

Enjoyed watching you solve this question. nice and outstanding

[Anonymous_Poetry]

Bro take log on both sides, can solve within a min,

[hannibal]

4:27 I have a question: If a/b=2/3, that means a=2 and b=3 so b-a=3-2=1, not 3, right? If someone knows pls tell me

[mijaelmarcelovillarroelchu]

Jugar con cartas suena interesante, pero creo que optare por ver documentales y resolver cubos rubit o tal vez hacer problemas de aritmetica pero de otro nivel, no se en donde encontrare ese tipo de cosas pero no se si habra otra mejor opcion para realizar un hobir matematico, espero tu opinion o algun consejo ya que tiendo a complicarme las cosas y por ello me quedo procrastinando con mi computadora que mucho me perjudica. Playing with cards sounds interesting, but I think I'll choose to watch documentaries and solve rubit cubes or maybe do arithmetic problems but on another level, I don't know where I'll find that kind of thing but I don't know if there will be another better option to do a hobby Mathematician, I await your opinion or some advice since I tend to complicate things and therefore I keep procrastinating with my computer, which greatly harms me.

[dr.blockcraft]

8a^a*b^b=27a^b*b^a
=1
(8/27)*(a^(a-b))*b^(b-a))=1
(8/27) *(a/b)^(a-b)=1
(a/b)^(a-b)=27/8
(a/b)^(a-b)=(3/2)^3

a-b=3
a/b=3/2
a=(3/2)b

(3/2)b-b=3
(3/2-1)b=3
(1/2)b=3
b=6
a-6=3
a=9

a²+b²=9²+6²=81+36=9(9+4)= 9(13)=90+27=117