Russia| A Nice Math Olympiad algebraic problem| Can you solve this?

This is a math Olympiad algebraic question. The algebraic identities were applied to solve the problem. #matholympiadproblem #algebra #mathematics

[@trugezi]

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[@JJONLINEMATHSCLASSchannel]

Ok. Thanks

[@jaybazu]

Don't be discouraged don't give up you are doing it great and we love you...

[@JJONLINEMATHSCLASSchannel]

Awww! I love you too. Thanks

[@hammadsirhindi1320]

You always pick wonder questions. Great job😘

[@JJONLINEMATHSCLASSchannel]

Thanks so much

[@johnstanley5692]

Could use synthetic division: let g1=a-b^2+111 (=0), g2=a^2-b-111 (=0). Note g1 is 1st order in 'a' so dividing g2/g1 eliminates 'a'. In this case remainder of g2/g1 =p4(b)= b^4 - 222*b^2 - b + 12210. Now 12210 = 2*3*5*11*37 -> p4(10)=0 & p4(-11)=0. This gives polynomial p2(b)=b^2-b-110 that divides p4(b) to return quotient, Q(b)=b^2 - b - 111; This means p4(b)=( b - 10)*(b + 11)*(b^2 - b - 111) => b = [-11, 10, 1/2 - 445^(1/2)/2, 445^(1/2)/2 + 1/2], & a = [10, -11, 1/2 - 445^(1/2)/2, 445^(1/2)/2 + 1/2]

[@JJONLINEMATHSCLASSchannel]

Thanks

[@olayinkaadeleye3134]

Elegant but you could have easily determined A1 and A2 with equation 3.

[@JJONLINEMATHSCLASSchannel]

Ok. Thank you

[@deme2259]

At 2.21 a-b should be put into brackets.

[@JJONLINEMATHSCLASSchannel]

Ok. Thanks

[@paulolemosmessias9460]

(a - b) ?

[@fernandoarielgarcia5498]

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[@MartinEbietey]

Can I get past questions to solve

[@JJONLINEMATHSCLASSchannel]

You can always source online.

[@shahidrasul9580]

I understood, you don't know about Extraneous roots.........😂

[@JJONLINEMATHSCLASSchannel]

My dear, after solving a mathematical question and then you substitute the root you got into the question and find out that it doesn't satisfy the equation,the root is said to be extraneous. As simple as that. I don't think it's worth making a video for cos it's just a simple thing to understand. Just ensure that after solving any mathematical question,that u substitute the solutions into the main equation to ensure that they satisfy the question. Anyone that doesn't is extraneous. That's all.

[@mugaggaibrahim2510]

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[@nadkhaa8360]

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[@JJONLINEMATHSCLASSchannel]

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