A beautiful math problem for advanced students | Equation Solving

What do you think about this problem? If you're reading this ❤️.
Also, i want to say sorry for a bad light during 1 minute. Thank You for understanding!
Equation: a^3 + a^2 = 36
Hello My Friend ! Welcome to my channel. I really appreciate it!
‪@higher_mathematics‬
#maths #math

[@rogerphelps9939]

Writting 36 as 27+9 presupposes you know the answer.

[@foopthethird5784]

This is a very general method of solving cubic equations. You take an answer that is obvious and reduce the equation to second order. I know it is not very elegant, however if you don’t know the cubic formula it is often the best you can do unless the equation offers you very very VERY special circumstances.

[@werbone]

I really wish people would stop using Olympiad as clickbait.

[@shred69]

Exactly

[@gibbogle]

A trivially simple problem for beginners. a=3 by inspection

[@user-xw4eu1hx1d]

Yes and then Horner's method to simplify and then discriminant to find the complex solutions.

[@reneeshcr]

a³+a² =36 a²(a+1)=36 a²(a+1)=9×4 a²>(a+1) By way of comparison, a²=9 and a+1=4 a=√9 and a=4-1 a=3 and a=3 Finally, a=3. It's just a different perspective.

[@HoSza1]

a=1? No... a=2? No... a=3? Yes!!! Let's divide a³+a²-36 ÷ a-3 = a²+4a+12. So the other two solutions: 2a=-4±√-32, two more complex roots a=-2+i√8 and -2-i√8.

[@1234larry1]

So, what you’re saying is: find the real root first, which by inspection or synthetic division is 3. Dividing by (x-3) gives you a quadratic, with two complex roots.

[@HoSza1]

@@1234larry1 Exactly! It often helps if you can reduce the degree of the equations. The same goal is behind using the rational roots theorem, often used in similar situations.

[@Fredscorpion2]

Trial and error 🤢🤮

[@Kndiani]

This method of solving the equation begins by guessing the correct answer! Why would anyone even continue once you got 27 & 9? That's your answer right there.

[@yehudaashkenazi5576]

This is not a mathematical way. If the answer was 1.23142765, then this method would not help.

[@Girl-dz8ck]

Your channel is very helpful

[@EnginAtik]

Re-write the problem as a^3=(6-a)(6+a) right hand side should be factorable by a therefore 6-a = 3 => a = 3.

[@jamesmcclure5947]

It took me all of 3 seconds to know a = 3.

[@groovermctoober4508]

I just looked at it, didn't even watch the video, and immediately saw that a = 3. It's so obvious.

[@prollysine]

by faktoring , a^3+a^2 |+/-| n*a-36=0 , / 3*12=36 , trial n=3 / , a^3-3a^2+4a^2-12a+12a-36=0 , (a-3)(a^2+4a+12)=0 , a-3=0 , a=3 , /// for complex , a^2+4a+12=0 , /// , test , 3^2+3^2=27+9 , 27+9=36 , OK , a^2+4a+12=0 , a=(-4 |+/-| sqrt(16--48)/2 , a=(-4 |+/-| sqrt(-32))/2 , a=(-4 |+/-| sqrt(32)i)/2 , a=(-4 |+/-| 2*sqrt(8)i)/2 , a= -2+sqrt(8)i , -2-sqrt(8)i , solu. , a= 3 , -2+sqrt(8)i , -2-sqrt(8)i ,

[@chrisclub3185]

To really solve this just write a^2(a + 1) and notice that if a were to be an integer, it’s square must divide 36, and the only squares that divide 36 are 4, 9, and 36, so a must be 2, 3, or 6, from there, check

[@MgtowRubicon]

a^3 + a^2 = (a^2)×(a + 1) = (3^2)×(3 + 1) = 9×4 = 36

[@dneary]

If you are given that the solution is in integers, then a^2(a+1) = 36 means a is in {1,2,3,6} - and process of elimination gives an answer. If you do not know that a is an integer, then you can try to identify where there are roots to a^3 + a^2 - 36 = 0 and you quickly get (a - 3)(a^2 + 4a + 12) = 0, or a = 3, -2 +/- 4✓(-2)

[@Ron_DeForest]

Awesome explanation. If you went with just the obvious answer you wouldn’t have found the imaginary numbers. What I want to know is why hasn’t anyone commented about the most obvious part of the video. Your crazy good hand writing. I’d love to be that legible.

[@Philihp1012]

Like they said, your solution presupposes to know the answer. Let’s do in another way. a^3 = 36 -a^2 = (6-a)*(6+a) Now, a^3 equals to a product of two factors; to get a product of two factors for a^3, you can decompose it this way only: a^2*a. Therefore a^2= 6+a and a = 6-a. From the second you get that a=3.

[@Girl-dz8ck]

Thanks ❤

[@drkimy]

a=3......I solve these in my brain!

[@harrymatabal8448]

a = 3 is one answer . I will use remainder and factor theorem to find the other 2. Your method is also an excellent method. Thanks

[@saeednazeri7480]

a=3 trivial solution

[@stevenconnell3206]

3 cubed plus 3 squared = 36

[@Open89182]

Can't we say a = 3 , is that wrong?

[@user-fv4jb5er6h]

27+9=36

[@_dolphine_]

Для чего дальнейшие рассуждения когда D

[@EMMANUELSOSU-hw3dm]

The value of a=3

[@rosbelisoropeza]

Ok. La idea es pensar. Usar los productos notables. Como tarea debe ser direccionada y contestar con explicaciones en cada proceso . Así un estudiante mejora su capacidad cognitiva.

[@jasonbarker1587]

I used substitution and found this answer in seconds

[@KyyTyy]

a³+a²=36 (x-3) (x²+4x+12)=0 (x-3) =0 x= 3 # (x²+4x+12)=0 (x+2)²+8=0 (x+2)²=-8 (x+2)=±i√8 x= 2±i2√2 #

[@Chris-5318]

Are these "Olympiad" problems intended for 7 year olds?

[@hervedumont6226]

I would like to see a rigourous démonstration. This is not the case here

[@MiguelSantos-ny8qz]

Pô!! Essa eu fiz de cabeça 😂

[@apopisso6302]

Bla bla bla bla bla. Don’t need nine minutes.

[@Ron_DeForest]

What are you getting from being a dick? You aren’t impressed, move on with your life. Don’t rip the guy for being thorough. Videos like these are for people who don’t have a masters in mathematics.

[@DragosStan1956]

For sure not beautiful and by no means for advanced students…

[@marcobsomer5574]

?

[@Fredscorpion2]

🤢🤮 a³+a²= 36 a²(a+1)= 9•4 a= ±3 a+1= 4 -> a= 3 (a³+a²-36)/a-3= a²+4a+12, a ∉ ℝ, a= 2(-1±𝒊√2)

[@lenudan]

"3" did it my head in like 10 seconds