China | A Nice Algebra Problem | Math Olympiad | A Nice Radical Problem

[@roberthayter157]

Excellent as usual! 😊

[@SALogics]

Thanks for liking! ❤

[@stas1ism]

Completely wrong

[@SALogics]

But how??

[@prollysine]

try , one solution among many , 162=27*6 , let u=V3^((Vx)/2) , let v=V3^((Vy)/2) , u^2-v^2=27*6 ,
(u+v)(u-v)=27*6 , let u+v=27 , let u-v=6 , u+v+u-v=27+6 , 2u=33 , u=16,5 , u^2=272,25 , v=u-6 , v=10,5 , v^2=110.25 ,
V3^Vx=272,25 , Vx=log(272,25)/log V3) , Vx=10.2069 , x=~ 104.181 ,
V3^Vy=110,25 , Vy=log(110.25)/log V3) , Vy=8.56126 , y=~ 73.2951 , solu , x=~ 104.181 , y=~ 73.2951 ,
test , V3^V(log(272,25)/log V3)) - V3^V(log(110,25)/log V3)) = 272.25-110.25 , --> 162 , OK ,

[@SALogics]

Very nice! I really appreciate that ❤

[@prollysine]

@@SALogics Thanks!

[@SALogics]

@@prollysine You're welcom! ❤❤