Russia | A Nice Algebra Problem | Math Olympiad

[@matheducare]

Excellent math. I love it very much.

[@SALogics]

Glad you like it! ❤

[@mfmohamad]

Good job

[@SALogics]

Thanks! ❤

[@SALogics]

Thanks ❤

[@nasrullahhusnan2289]

(x^⅓)+(x^½)=4/27
Let t=x^⅙ --> t²+t³=4/27
=(3/27)+(1/27)
=(1/9)+(1/27)
=(⅓)²+(⅓)³ --> t=⅓
As t=x^⅙ --> x=t⁶
=(⅓)⁶
=(⅓

[@SALogics]

Very nice trick! ❤

[@davidseed2939]

you did need to consider x_2 because the negative y could only work if you had a negative x but you can't.
so all you needed to do is look at y³ +y² =1/27 + 1/9
y=1/3, sqrt(x)=(1/3)³

[@SALogics]

@@davidseed2939 Very nice! ❤❤

[@user-qr7dw4hk6x]

Да 1/3 можно сразу подобрать, это будет один корень, потом кубический разделить на х-1/3, получим квадрмтный и , собственно , все.

[@ivanandronov7529]

1/3^(1/6)

[@محمدالنجار-و2ف]

The second value does not verify the equation.

[@SALogics]

You are right! ❤

[@trojanleo123]

x = 1/729

[@SALogics]

You are right! ❤

[@MananArhamOP]

Bro, listen to me. I am your big fan, but can u tell me why these equations are named after countries?

[@SALogics]

Because these questions are from international exam cometitions math olympiad ❤

[@irenehartlmayr8369]

Obvious answer. JUST THINK !..

[@textonashford3309]

Error. Should be +1/27

[@SALogics]

Where, I can't understand???

[@AlexD02721]

Why are so many people writing ‘x’ like this these days?

[@SALogics]

Because this looks great! ❤

[@mauriziograndi1750]

Alternatively:
4/27 = is given.
4/27^1/4^1/3^1/3^1/3
=
1/729 = 0.00137…
Answer

[@SALogics]

Very nice! ❤

[@Xjxtimvbhf-ujnjdmczrdjqyt]

Где третий корень, чудила?

[@SALogics]

Второй и третий корень одинаковы, дорогая! ❤

[@Xjxtimvbhf-ujnjdmczrdjqyt]

@@SALogics Не поступил, дорогая.

[@yakupbuyankara5903]

X=1/729

[@SALogics]

Yes, you are right ❤