Olympiad Algebra Problem | Math Olympiad Questions

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Maths Black Board

Maths Black Board

Күн бұрын

Пікірлер: 10
@dacmaxin
@dacmaxin 2 ай бұрын
It's directly visible, all variables are 1. But I like your approach, it teaches other concepts as well.
@farrukhuddin424
@farrukhuddin424 2 ай бұрын
1
@mdlelim4234
@mdlelim4234 2 ай бұрын
3
@technopanipuri3054
@technopanipuri3054 2 ай бұрын
One could guess just by looking that the solution of both equations is 1
@satrajitghosh8162
@satrajitghosh8162 2 ай бұрын
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
@niranjanchakraborty1139 2 ай бұрын
Ans=1
@hariomdas270
@hariomdas270 2 ай бұрын
1+1+1=3 1^2+1^2+1^2=3 1^2021+1^2022+1^203=3
@shivshankar2475
@shivshankar2475 2 ай бұрын
A=b=c= 1 So last answer is 3
@mohanjitsingh1163
@mohanjitsingh1163 2 ай бұрын
Good one.
@AnjanBiswas-bc2mk
@AnjanBiswas-bc2mk 2 ай бұрын
My goodness!! Is it the way to solve this problem? You will get hardly 5 seconds for this
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