Mexico - A Nice Math Olympiad Exponential Problem

Why do these channels never state that they are only seeking real roots at the beginning? 😡

For all functions of type f(x)=ax^3+bx+c the equation f(x)=0 can have only one real root in case of a>0, b>0, because f'(x)=3ax^2+b>0 and therefore f(x) is monotonically increasing. Also, if the equation f(x)=0 has rational roots in the form p/q, p is a divisor of c and q is a divisor of a. If a=1, the rational roots are always whole numbers. One can immediately see that in the specific example f(y)=y^3+y-130=0 , y=5 is a solution, because we first check the whole divisors of 130 (+-1, +-2, +-5, +-10, +-13).

Try to solve x^7+x^5+x^3+x=170 with your method....No chance. With above, you show that x=2 is the only root in just 2 rows.

I hate log, because every time you calculate the log, it is impossible to calculate by yourself without calculator.

not correct

Use logs.

when you apply log base 5 instead of log base 2🤣

2^x=5

Now solve 8^x + 2^y = 130. 😅

Facevi prima con Ruffini

She is not solving math problem she is making math problem.

I dont have money to go university, but i can solve that math

Gives me shivers, brings back nightmarish memories of struggling with all this in school years!😮
But enjoying it too, in a contradictory way, because there is no pressure!😊

2.3219281

I got from a much easier and faster way 2*3x and 2*x should be equal to 130 so the sum of two of 2 power something should be equal to 130 which is close to 2*7 hence if x=2 the answer is 64+4 and if x= 3 it would be 528, therefore, x should be between 2 and 3 and closer to 2 than 3 and 3x kinda feels be close to 7 as 128 is close to 130 so 7/3=2.33 and as it wouldn't add up (cuz 127+4,9 is greater than 130 we should decrease 2,33 by 0,01 per time to find the right answer then we got the answer of 2.32

The definition of the logarithm is "to what power do I need to raise value1 to get value2. So you could write from start that x = log(2, 5).

Was in it better to approximate x between 2 and 3 at a glance?

@vipo1
há 0 segundo
Hi Teacher; I am sorry, but you go around and around, and around with the logarithmics, you can simplify A LOT it if you apply the rule that ... a^b ... or ... a.exp(b) = b.log(a) <<< - consider base 10, it is easy for tables...
It seems you want to show all the logarithmics rules ...

In solution checking
a^(log c to base a) can be written as c^(log a to base a) .
So 8^(log 5 to base 2) can be written as 5^(log 8 to bas 2), which is 5^3 and 2^(log 5 to base 2), is 5^(log 2 to base 2) which is 5
5^3+5=130

x ~ 2.321
I used calc and brute force 😂

Whatttttt

are you serious this easy question can solve anyone

I remember fondly a time where maybe, just maybe, I might have had some idea, but I haven’t used anything beyond grade 9 algebra in 20 years.

That's why I failed math. It's confusing.

Why is this in HDR lmao

Change of bases can be used to simplify the final expression

8^log_2(5) = (2^log_2(5))^3 by associativity and commutativity
=5^3 since x^log_x(a) = a
=125

And the same with the other term, so
125+5 = 130

I have simplier solution. Multiply both by root x, so then 8+2 = x base root of 130. Which easily = 2.3....

It's easy so 😂😂

..am I the only one to solve it in their mind after seeing the thumbnail?

Lk Logic well know to get views in the name of fake olympiad level questions too easy for olympiad

Thanks,

this is extremely easy for an olympiad question

Вообще тут сразу видно, что два в кубе и в степени х. Далее рассуждаем какое число в кубе ближе всего к 130, сразу понятно что 5. 125+5 как раз 130. Ну а далее изи вообще 2 в степени х равно 5. Это тоже в уме решается понятно же что два в квадрате это 4, а в кубе 8. Стало быть показатель степени будет дробный. Рассуждаем нужно умножить двойку на себя чуть больше двух раз примерно на треть и получаем что x примерно равен 2,33. Ну или через логарифм можно записать. Офигеть олимпиадная задача 😂

Can't we just use log on both sides?

I think it's not of Olympiad standard . Btw I am Indian , so we often do these problems in school . ( Please don't get offended)

a=2^x
a^3 + a = 130
both increasing
a=5 is the only solution
2^x = 5
x = log 2 (5)
:/

Just looking at this I can see the answer is going to be 2 and a bit

we learn this when we go university how this is olmpyic af

عالی بود ، استاد ❤
🇮🇷

Bruh that’s not olympiad, that’s Asian high school students’ exam

Too easy

It’s hard 😂

A little bit easy for asian student 😅

The video started dropping frames as the plot got thicker. 😂

You dont need to use calculator to check the answer.

Bijayathspa

Substitution is way better to find solution. 1 2 3 4 5😂😂😂

The sex must sucks.