Math Olympiad | A Nice Exponential Problem | 90% Failed to solve

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[@superiorlyrics8326]

👏👏

[@crazyindianvines1472]

nice

[@mikelivstone]

Just out of curiosity, did you try just using the quadratic formula?

[@Rocio62154]

SENSATIONAL PROFESSOR!!

[@vijaymaths5483]

Thank you ⚘️

[@mayurbhaigalaiya578]

It can be solved easily as follows:
44444442222222=2222222+4444444*10^7

[@dominiquebercot9539]

Autre méthode
On a 44444....22=x(x+1), donc racine de 44444...22 est compris entre x et x+1
On calcule cette racine, à l’ancienne, par approximations successives. On trouve que le premier chiffre à gauche est 6, suivi d’un autre 6, puis encore 6....il n’y a plus qu’à vérifier que 666666^2+6666666=44444....22