Japanese | Math Olympiad | A Nice Algebra Problem

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[@CTJ2619]

i enjoy your videos . I am stuck at home with covid and it is fun to watch your process with this problem . I am a retired math teacher

[@bobbyheffley4955]

The final result can be found in the area formula for a regular octagon: A=2*(1+sqrt 2)s^2.

[@ЛидийКлещельский-ь3х]

[x+y*sqrt(2)]^3=…=(x^3+6*x*y^2)+(3*y*x^2+2y^3)*sqrt(2)=99+70*sqrt(2) .Therefore (1) x*(x^2+6*y^2)=99 ; (2) y*(3*x^2+2*y^2)=70 . (3) x=3*u (4) y=2*v .We substituted (3) in (1) end (4) in (2) . We get : (5) u*(3*u^2+8*v^2)=11 ; (6) v*(27*u^2+8*v^2)=35 . You can guess, that : !!! u=v=1 !!! We get : !!!! x=3 , y=2 !!!! Therefore : [3+2*sqrt(2)]^3=99+70*sqrt(2) .
3+2*sqrt(2)=[1+sqrt(2)]^2 .
We get your answer !!!
With respect , Lidiy

[@gilbertogarbi4479]

Awsome!

[@노을-z8d]

잘보고 있습니다

[@Haloperidol-7]

Здорово!

[@peterotto712]

Dünndvhiss