Olympiad Algebra Problem | Math Olympiad Questions

[@dacmaxin]

It's directly visible, all variables are 1. But I like your approach, it teaches other concepts as well.

[@farrukhuddin424]

1

[@mdlelim4234]

3

[@technopanipuri3054]

One could guess just by looking that the solution of both equations is 1

[@satrajitghosh8162]

Generalized problem a + b + c = m, a^2 + b^2 + c^2 = m^2/3 2 ( a b + b c + c a) = ( a + b + c) ^2 - ( a^2 + b^2 + c^2) = m^2 - m^2/3 2(a^2 + b^2 + c^2) - (a b + b c +c a) = 2 m^2/3 - 2 m^2 /3 = 0 ( a - b) ^2 + ( b - c) ^2 + ( c - a) ^2 = 0 a = b = c = ( a + b + c) /3 = m /3 Hereby a^(2021) + b^ (2022) + c^ (2023) = ( m /3) ^ (2021) * ( 1 + a + a ^2)

[@niranjanchakraborty1139]

Ans=1

[@hariomdas270]

1+1+1=3 1^2+1^2+1^2=3 1^2021+1^2022+1^203=3

[@shivshankar2475]

A=b=c= 1 So last answer is 3

[@mohanjitsingh1163]

Good one.

[@AnjanBiswas-bc2mk]

My goodness!! Is it the way to solve this problem? You will get hardly 5 seconds for this