Как прекрасен язык математики. Всё понятно, подробно объясняно. Учитель супер. Спасибо за ролик.
@michaelhuppertz6738Ай бұрын
Nice solution specially how got the (x-3) out of 6x^3+18x^2, neat trick.
@ajmiller710223 күн бұрын
Excellent. Straight to the solutions. Well done!
@NadiehFan27 күн бұрын
A different approach which does not require a substitution and which does not require having to deal with fractions starts by multiplying both sides by (x − 3)² to get rid of the fraction. We can then proceed as follows x²(x − 3)² + 9x² = 16(x − 3)² x²(x² − 6x + 9) + 9x² = 16(x − 3)² x²(x² − 6x + 18) = 16(x − 3)² (x² − 3(x − 3) + 3(x − 3))(x² − 3(x − 3) − 3(x − 3)) = 16(x − 3)² (x² − 3x + 9)² − 9(x − 3)² = 16(x − 3)² (x² − 3x + 9)² − 25(x − 3)² = 0 (x² − 3x + 9 + 5(x − 3))(x² − 3x + 9 − 5(x − 3)) = 0 (x² + 2x − 6)(x² − 8x + 24) = 0 x = −1 + √7 ⋁ x = −1 − √7 ⋁ x = 4 + 2i√2 ⋁ x = 4 − 2i√2
@laurentbeyer245827 күн бұрын
I would have done same 👍🏻
@TapanDas-ei3lw20 күн бұрын
You're also a great genius ❤❤❤
@michellewelchman9245Ай бұрын
I enjoyed your work and your explanation. Excellent and well done! These problems can be long and it took nearly three pages for this one! Lol Sometimes it feels like you're going down a math rabbit hole with no end but in the end when you do reach a solution (s) it's all good.
@peterbyrne639419 күн бұрын
Thank you. very nice solved equation.
@oxfordmathseries24 күн бұрын
I prefer to get rid of fraction first, then solution will be of 2 minutes only
@Ron_DeForest23 күн бұрын
Would have been way faster and easier. So much less time to multiply through then gather terms.
@NadiehFan27 күн бұрын
Yet another method is to note that (x − 3)² = x² − 6x + 9 and therefore x² = (x − 3)² + 6x − 9 so we can rewrite the equation x² + (3x/(x − 3))² = 16 as (x − 3)² + 6x − 9 + (3x/(x − 3))² = 16 or (x − 3)² + 6x + (3x/(x − 3))² − 25 = 0 Here (x − 3)² + 6x + (3x/(x − 3))² is a perfect square because 6x is twice the product of (x − 3) and 3x/(x − 3) and we also have 25 = 5² so we get ((x − 3) + 3x/(x − 3))² − 5² = 0 which gives us a difference of two squares at the left hand side whereas the right hand side is zero. This allows us to factor the left hand side using the difference of two squares identity and then apply the zero product property. However, before doing so we first multiply both sides by (x − 3)² to eliminate the fraction so we get ((x − 3)² + 3x)² − (5(x − 3))² = 0 (x² − 3x + 9)² − (5x − 15)² = 0 (x² + 2x − 6)(x² − 8x + 24) = 0 x = −1 + √7 ⋁ x = −1 − √7 ⋁ x = 4 + 2i√2 ⋁ x = 4 − 2i√2
@ahadjonxamidov894027 күн бұрын
Zo‘r
@martinreichard324327 күн бұрын
I prefer to take the square root first and then expand with x-3. This is faster.
@lenchorivera85436 күн бұрын
Me estoy acordando de mis clases en la prepa…
@louiskah47532 күн бұрын
C'est une identité remarquable ❤
@TapanDas-ei3lw20 күн бұрын
Never ending marathon mathematics and brain 🧠 puzzled stories ever. Einstein newton and all superb mathematicians brain to be needed to understood not like me the stupid one..not getting any sweet juice extract from your mathematics, all energies i have lost to get it understood sir .really sir you've the genius brain and you're great.❤❤❤after this life i shall pray to God ,make me genius like you.❤❤❤❤❤
@user-cc4zk1ec8c23 күн бұрын
It can be solved by converting x to a trigonometric function. (x/4)^2 + (3x/(4(x-3)))^2 = 1 x/4 = cos 3x/(4(x-3)) = sin 16(cs)^2 - 18cs - 9 = 0
@mahmoudibra582221 күн бұрын
Beautiful
@learncommunolizer20 күн бұрын
Thank you very much
@user-ix3lv9qz5b23 күн бұрын
It's a troubled solution.
@tamarshahverdyan272316 күн бұрын
# 30 #
@spelleg11Ай бұрын
Great.
@mohamedsalah5525Ай бұрын
4-
@samswift492126 күн бұрын
C 1.4 hrs or 84 minutes.
@rajanisarmah630720 күн бұрын
Aare vaai itni si sota math aur kitna lomba korega??
@TheTeller201221 күн бұрын
X-x/3-1=0
@user-vo4qp5bm7p21 күн бұрын
Почему в ответе Вы сократили на 2..???? Так нельзя!!!
@tatyanasnisarenko162720 күн бұрын
Х=2
@bandoubenamar28028 күн бұрын
I no 😂
@divineinspiration334226 күн бұрын
Spreco di carta
@anuarsalomao974825 күн бұрын
COMPLICADO
@anuarsalomao974825 күн бұрын
MAS É ORGANIZADO
@jamielunes184129 күн бұрын
I want to hear a German 😂
@Limited_Light23 күн бұрын
Warum sagen sie das?
@himadrikhanra746322 күн бұрын
1/10..?
@VikasKumar-bj3ru4 күн бұрын
Kya bakwass hai yo seedha asnwer ara iska binomial se