Germany| A Nice Math Olympiad exponential question| Can you solve for x?

[@marcgriselhubert3915]

1/3 is evident solution, so we can fctorize:
x^3 + x^2 -4/9 = (x - 1/3).(x^2 +(4/3).x +(4/9))
= (x -1/3). (x + 2/3)^2.
So the given equation has two solutions:
1/3 (simple solution) and -2/3 (double solution).

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[@soumayahatchi4168]

Love you too darling . Thank you for teaching us a smart and easy way of solving math problems

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U are welcome

[@jmich7]

And your expressions are so funny, SUPER COOL!

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Thank you

[@Rich-Man820]

Wonderful

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Thanks

[@RyanLewis-Johnson-wq6xs]

(0.3/0.9)^3+(0.3/0.9)^2=0.148/0.999=4/27 (-0.6/0.9)^3+(-0.6/0.9)^2=0.148/0.999=4/27 x=0.3 recurring or 1/3 x=-0.6 recurring or -2/3

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👏👏👏

[@prime423]

Look at the original equation!!Its clear 1/3 is a root. Then use synthetic division. Simple,with very little angst. Simple is always better!!

[@johnstanley5692]

given x^2*(x+1) = 4/27 = (2/3)^2 * (1/3) = (2/3)^2 * (1-(2/3)) => (3*x+2)|g(x), where g(x)=x^2 * (x+1) - 4/27 (=0).
dividing g(x) / (3*x+2) = (1/27) * (9x + 3 *x - 2) => g(x)=(1/27)*(3*x + 2) * (3*x + 2) * (3*x - 1)=0 => x={ -(2/3), - (2/3), (1/3) }

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[@shahidrasul9580]

your methods are very Smart ❤

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Thanks so much

[@hungriafeliz8885]

Después de la factorizacion

[@pukulu]

x = 1/3 by inspection but there are also a couple of other roots.

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Nice guess

[@LifnaCabi]

Muito inteligente,mae, fantastica didatica!Guine-Bissau.
Traduzir em ingles.​@@JJONLINEMATHSCLASSchannel

[@fernandoarielgarcia5498]

You are a super smart girl💖😘😘🥇

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Thank you

[@elmoussadekelaoufir144]

Sorry you can solve with more easily you can separate 4 from 1 and 3.....

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Ok. Please drop the method. Thanks

[@elmoussadekelaoufir144]

I solved this equation in 3 minutes

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🤝🤝

[@jeankouassi5897]

I like your smile.

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Thanks

[@hungriafeliz8885]

Favor .iras debajo falta un parentesis

[@hungriafeliz8885]

Quise decir que falta un paréntesis después de la factorizacion del primer polinomio

[@hungriafeliz8885]

Re