Can you solve this?| A nice math exponent simplification
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- Опубліковано 25 кві 2024
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25 - 4 = 21 √m/2 = 2 m = 16
And what is a 21 and 1
Very nice solutions
Thank you 😊
This is easier to solve with observation,not perspiration!!5 squared minus two squared is 21.10 seconds not 10 minutes.Mathletes should use "Tricks" only when needed !!
To be complete also develop x=21 and y=1
Good solution. Not come at a time
m is supposed to be a positive integer. Otherwise we have two answers. One is m=16 the other is
m=(4ln11/ln5)^2.
I found the derivative and convinced myself that the function is increasing. [even by just looking at the function it is simple to be convinced that it is an increasing function] m=16 easy to guess. Your way is obviously more matamatical.
Actually, your solution is shorter and more rigorous. Combination of guessing and uniqueness proof is perfectly ``mathematical".
Muy complicado tu solución
Es más sencillo igualar en vez de 21 a 5^2 - 2^2 y por bases iguales en ambos miembros se despeja "m" de una forma rápida
Where is write that (x+y) and (x-y) has to be integer???
It's not. It just happens (luckily) for this solution approach that they are integers.
f: m ---> (sqrt(5))^(sqrt(m)) - (sqrt(2))^(sqrt(m)) is strictly increasing on R+, so if the equation f(m) = 21 has a solution then this solution is unique. Now as 25 - 4 = 21 it is evident that m = 16 is a solution. Finally m = 16 is solution and it is unique. That's all !!!
It's only another cuadratic equation
16.
Собственно, задача простая, как большинство Диофантовых. Тут сразу видно, что m делится на 4 и должно быть полнись квадратом . Это или 16 или 36. функция слева -возрастающая и 36 - много. Всё.
U=2
m=16
(√5)^(√m) - (√2)^(√m) is clearly an ever increasing function as m increases from 1 to infinity. Therefore there is at most one real value of m such that (√5)^(√m) - (√2)^(√m) = 21.
By observation, m = 16 satisfies the equation and it is therefore the only value that does when m ≥ 1.
If m < 0, then there are no real solutions.
If m = 0, then there is no solution either.
Consider 0 < m < 1.
So, 1 < (√5)^(√m) < √5 and
1 < (√2)^(√m) < √2
So (√5)^(√m) - (√2)^(√m) < 21 So there are no solutions to be found here.
So, m = 16 is the only real solution to the given equation.
It should be mentioned here that solve this for integer value of m
By hit & trial we know 25-4=21 so m=16
It has an infinite number of Solutions.
“Fantastic explanation! I love how you break down complex concepts. I do similar math tutorials and challenges on my channel. Check it out for a fresh perspective on math problems!”
Thank you 😊. Sure I will check it out!
Это проще решит "в уме" методом банального подбора
x=16, solved in 4 sec
really? is that the time it took you to slide the cursor directly to the end of the video ? if not, please explain what you could have possibly thought in the short period of 4 sec, after reading that and saying "yep thats 16" 😂😂😂
@@mijazukant first tried by 2 then I got the wrong answer, then 4
But I aware then that it's in root number
So, I multiply 4 with itself to get the solution
Manakanakku m=16
А что если данное решение не единственное?
Решение единственное, что видно из условия.
Но ведь может быть такой вариант: x=11, y=10. Как решать в таком случае?
Вагон ошибок
это в каком-то смысле подбор. А если бы не целые числа были? А если бы не 5, 2, 21, а сотни или тысячи?
Так вообще можно было 1 мин 38 сек записать, что 5^u - 2^u = 25 - 4 => 5^u - 2^u = 5^2 - 2^2 => u=2, и не тратить ещё 6 минут
Не знаю, как сейчас, но когда я учился в школе, такое решение не зачли бы.