China | Can you solve this? | A Nice Math Olympiad Algebra Problem
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- เผยแพร่เมื่อ 17 ก.ย. 2024
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How to solve this math problem
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Thanks, but it is too long.
Once you got 'ab = 3' then you could substitute into the given 'a-b = 2' which would yield 'a^2 - 2a - 3 = 0', thus a = -1 and +3. Finally x+13 = (-1)^3 and (3)^3, that is, x = -14 and +14.
So precise and orderly. Really help this 74 year old to keep his brain percolating. Thanks!
Imagine everlasting life and what you personally doe ? This will give you an idea 💡 on how to get it
+ 16 All Scripture is inspired of God+ and beneficial for teaching,+ for reproving, for setting things straight,+ for disciplining in righteousness,+ 17
He solved it in an overly-complicated manner. All those extra equations and manipulations aren't needed. Simply cube each side and simplify, then substitute a part using the original equation, and finally solve for x. It's so fast that I created a general solution to solve these types very easily.
The cube of a binomial has the following form:
(m - n)³ = m³ - 3*m²*n - 3*m*n² - n³
(m - n)³ = m³ - n³ - 3*m*n*(m - n)
Factor (m - n) on the right is what was cubed, and that's given as b in the original equation:
³√(x+a) - ³√(x-a) = b
(³√(x+a) - ³√(x-a))³ = b³
(x+a) - (x-a) - 3*³√(x+a)*³√(x-a)*b = b³
2*a - 3*³√(x²-a²)*b = b³
2*a - b³ = 3*³√(x²-a²)*b
(2*a - b³)/3/b = ³√(x²-a²)
((2*a - b³)/3/b)³ = x²-a²
((2*a - b³)/3/b)³ + a² = x²
x = ±√(((2*a - b³)/3/b)³ + a²)
For this problem, a = 13 and b = 2 :
x = ±√(((2*13 - 2³)/3/2)³ + 13²)
= ±√(((26 - 8)/6)³ + 169)
= ±√((18/6)³ + 169)
= ±√(3³ + 169)
= ±√(27 + 169)
= ±√196
x = ±14
I generated my own math problem:
³√(x+100) - ³√(x-100) = 5
The solutions checked out on my calculator:
x = ±45*√5
La explicación paso a paso, larga, pero aclara muchas dudas y hace razonar para bien. Gracias 👌👏👏
Imagine everlasting life 5:47 + 16 All Scripture is inspired of God+ and beneficial for teaching,+ for reproving, for setting things straight,+ for disciplining in righteousness,+ 17
Bueno, me apasionan las matemáticas, y en ese idioma puedo hablar, también en castellano....y nada más, disculpas.
красиво решает как стихи пишет, с удовольствием смотрю
İ think you chose the largest way 😂
A*2+ab+b2=13
A-b=2
(A-b)^2=a^2+b^2-2ab =4
3ab=9 a.b=3
So (a+b) ^2=16 a+b=4,-4
Lovely solution
Great solution
Better beneral solution:
³√(x+a) - ³√(x-a) = b
x = ±√(((2*a - b³)/3/b)³ + a²)
Verry nice! As always!❤
Love from Bangladesh ❤❤❤
короче решается
зачем город городить, решается за 2 минуты
имеем 'a-b = 2' находим b = a-2 и сразу подставляем в 'a^2 + 2ab +b^2 = 13 самом начале
решаем квадратное уравнение и находим a = -1 и +3.
затем возводим a^3 = x+13 и решаем находим x
Bravo!
Carefully peruse this equation. There are two cube roots that differ by two. Its easy to find 14 as an answer. Sometimes inspiration is better than perspiration!!
But you missed the other solution.
I think you can solive this problema with a_b=2 and a.b=3.thank you very much.
You ought have applied quadratic solution from where you got ab=3 and a-b=3 to abridge the long route but great work
Yes, I was also thinking that.... He perhaps wants to make his video longer... 😅😅
The whole problem can be solved by cubing the original equation, simplifying, replacing 2 terms with the constant of the original equation, and then solving with basic math.
³√(x+13) - ³√(x-13) = 2
2*13 - 3*³√(x²-169)*(³√(x+13) - ³√(x-13)) = 8
18 = 3*³√(x²-169)*(2)
3 = ³√(x²-169)
27 = x² - 169
196 = x²
x = ±14
General solution:
³√(x+a) - ³√(x-a) = b
x = ±√(((2*a - b³)/3/b)³ + a²)
Bye Bye
x = 14 or x = - 14
Yep. Solved it before the video even loaded
asnwer=13 /2
wait i don't get it. why do we have to do the expansion at 4:45?
Actually, that's the only thing needed to solve the problem. Cube both sides of the original equation, and simplify. Note that (a - b) is a factor, which is the constant of the original equation, so replace it. The rest of solving for x is just basic math. He didn't need to introduce all those other equations and formulas.
Зачем городить такой огород? Решается элементарнр заменй переменной x´+13´=t^3.
X=14
x = ±14
Il est faux de dire que √16 = ±4, la racine d'un nombre étant toujours positif, il faut dire ±√16 = ±4, je remarque que tu fais souvent la même erreur 🙄🙄
FYI, √16 = 4 and ±√16 = ±4 .
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