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Пікірлер
"Что-то умное про подбор"
This is the righ way to solve such question. Of course in this example is easy to find 3 as solution. But in general case , this is the right way to solve, mainly when the the solution is not a integer number.
perfect.....
(-9;8)(8;-9)
Why not just replace -y by x+1 in eqn (1) once we get x+y+1=0?
Set x=y-3. It will be easier to solve y.
Correct
Hi, can you solve x³+x²=27 ? Thank you!!
The mean/median of x, x+2, x+4 and x+6 is x+3: so to restore some symmetry i'd be tempted to let u = x+3 from the outset so that the equation becomes (u-3)(u-1)(u+1)(u+3) = 9. Hence (u^2 - 1)(u^2-9) = 9 so u^4 - 10u^2 = 0 so u^2( u^2 - 10) = 0. This gives u^2 = 0 or 10 or equivalently u = 0 or ±sqrt(10) and so x = -3, -3 ±sqrt(10)
👍 thank you
1/4
X = -3
Let x = u - 3 and let's find the integer solutions (if they exist). So, (u - 3)((u - 1(u + 1)(u + 3) = 9 So, (u³ - 1)(u² - 9) = 9 So, u² is 0, so u is 0, as u² - 1 and u² - 9 are factors of 9. So x = - 3. In fact, this is a double root of the original formula and we are left to find the other two solution, which are non-integer but could be complex solution, since the original equation is a quartic equation. So we could expand the original equation and divide it by (x + 3)² to find the remaining quadratic formular and then solve it using the quadratic formula.
x=-3
You are being fooled with this nonsense! This method only works if you know the solution in advance. You need to split a number like 30 into two numbers x and y, such that x + y = 30 and 3^x = y (ie. 3 +27 = 30 and 3^x = 27), where x must be the solution you are trying to calculate. In other words, you need the solution of the problem in order to successfully follow the last steps. For example, if you try to solve 3^x + x = 40, you just need to split 40 into 3.279887… (the solution to the exercise!) and 36.72011..., both irrational numbers (infinite decimals), since 3.279887… + 36.72011... = 40 and 3^3.279887… = 36.72011... Brilliant method!
Have you tried your solutions into the original equation? I can't make them work. I think you made a mistake when cancelling squares with square roots. To me the problem has no solution: √x + √(-x) = 2 √x + √((-1)x) = 2 √x + i √x = 2 Here, the real parts on both sides of the equation have to be the same, and also the imaginary parts have to be the same. That's not possible, so there are no solutions.
Solved beautifully
Solved nicely sir
Hi! I only factored the expression to solve it but it's nice to see your excellent algebraic solution which can be a tool for me/everyone to solve further mathematical problems. Thanks!
Nice explanation
good approach
Easy
Very easy
If you cannot speak english like a native american, do not try to, you keep making a fool of yourself.
Very intresting
Excellent solution
There is noting to solve here, this is already a number, not an equation.
2:21 : I left the chat
Nice❤
not correct 255/16
I am about to comment the same
255/16
Solved it smoothly
As a generalization, the method presented always works if in the equation a^x + x = b one has b = a^a + a, with the solution x = a. Try it out with some numbers or repeat the derivation as in the video.
sometimes there is no need to think a lot. the first thought after looking is correct answer so no need to over complicate.
...chłopie, po co tyle pierdolenia ?!...a+b=-1 -> a=-b-1 wstawiasz do drugiego równania i masz równanie kwadratowe z b -> { (-9,8); (8,-9)}
Nuevo suscriptor. gran problema de algebra, apoyo mutuo. like
нахуя а главное зачем
Ты крут, люди считающие, что ты всё усложнил просто смешны. Да, здесь x легко находится подбором, но посмотрим на них, когда в следующий раз x окажется не целым числом, например.
Биномиальный поиск
да и плюс когда решаешь алгебраически, то находишь все корни уравнения или (как здесь) доказываешь, что корень только один. решая подбором ты никогда не можешь быть уверен, что у уравнения не может быть ещё какого-то корня, который ты не учёл. подбор - всегда неполное решение, т.к. ты не доказываешь, что больше корней нет. геометрическое решение тоже не всегда верно, т.к. оно показывает пересечение графиков функций на действительной плоскости, а как быть уверенным, что у уравнения нет ещё дополнительного комплексного корня? его не изобразить геометрически, почти невозможно найти подбором, а решая такое уравнение алгебраически, ты всегда на 100% находишь все корни и никто не подкопается
Всё супер
It doesn't even have to be an integer! The split 30 = 3 + 30 requires the solution (eg. 3) that you are looking for. If you don't know the solution, you can't use this method.
Сумма двух возрастающих функций - возрастающая функция, так что тут очевидно только одно решение. Так что это явное переусложнение. Если бы ответ был нерациональным чистом, тогда и стоило бы так решать
Bro doesn't search for easy ways
Actually when I wrote this I had no idea how to solve this and neither I do now. Sorry
The WORKING easy way is make graphs of functions 3^x and 30 - x. With this graph we can prove that this equation has only one solution. People can just understand it's 3, but robots will use perfect made graph for it
x=y=10
b= -9 a=+8 and vise vers.
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bro u can do it easily by binomial expansion of (1+.005)^200 its first and second term are both 1 and we are done
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Excellent!
Thank you ❤️
Very nice ❤
Thanks 🤗
Thank you
Not bad, but maybe change the base from 2 to something else if it's even possible to do so. This was too easy to solve by thinking alone, 2048 - 16
11^33*2^33 vs 11^22*3^22 Refactor Divide by 11^22 and 2^22 yields 11^11*2^11 vs (3/2)*22 22^11 vs (9/4)^11 Change base and exponent and compare bases 22 vs (9/4) so 22^33 is larger
thank you 🙂🙂