Japanese | Can you solve this ? | A Nice Olympiad Algebra Problem

[@JawadTalb-eu2ee]

😊😊

[@mariosanagnostou3298]

it's more simple if you observe that a-b=1 then you know (a-b)^2=1 and you have a^3-b^3=1 . Finally you find ab=0. The next is simple

[@johnstanley5692]

let y=(x-3)/(x^2+3) and note that (x^2+x)/(x^2+3) = 1+y (use synthetic division if this is not obvious). Problem maybe written (1+y)^3-y^3-1=0 expand to obtain 3*y^2+3*y= 0 , y=0 or y=-1; y=0=> x=3, & y=-1 => x^2+x=0 or x = 0, or x=-1,

[@belengenicio8606]

Muy bien.

[@learncommunolizer]

Thank you very much 🙏❤️

[@maksymkorinnyi7576]

Eksi....😂

[@murvetaykac7041]

You told that solition very well.Thank you.

[@АндрейПергаев-з4н]

Если умножить на знаменатель, то не надо возиться с дробями

[@AlbertHu-u9o]

It just need patience

[@Nikos_Iosifidis]

Nice problem

[@АндрейПергаев-з4н]

Если присмотреться то если из первого числителя отнять второй равно знаменателю, это не зря

[@shmuelzehavi4940]

Another method: The original equation is: ((x^2 + x) / (x^2 + 3))^3 - ((x - 3) / (x^2 + 3))^3 = 1 (1) This equation may be written as: a^3 + b^3 + c^3 = 0 , denoting a, b, c as: a = (x^2 + x) / (x^2 + 3) , b = - (x - 3) / (x^2 + 3) , c = -1 Is easy to show that: a + b + c = 0 and in this case: a^3 + b^3 + c^3 = 3abc = 0 . Therefore, eq. (1) reduces to: ((x^2 + x) / (x^2 + 3)) ((x - 3) / (x^2 + 3)) = 0 (2) However, x^2 + 3 ≠ 0 and therefore eq. (2) reduces to: x (x + 1) (x - 3) = 0 which gives 3 roots: x=0 , x = - 1 , x = 3

[@samuelbenet007]

Un truc que je voudrais voir sur tes vidéos, c’est le domaine de définition. Ici par exemple : X^2-3≠0 ===> Df = R - { -√3 ; √3}

[@mathsfamily6766]

please more equation like this ! I love this so much

[@kizerCoundSlouder]

How about the same equation but make it functional?

[@comdo777]

asnwer=x1 isit

[@AnisYousuf-w8u]

Kwerage tight ywello wy werji x aydelem xsquaru yishalegnal middre chikko azawoch ekhkhkhkheeey yihe dirty ymiyasetella bahriyachun bmin y9gelets y9hon ainstien rasu binor qala5 yattalet nbere kirfatamoch