Mathematical Olympiad | Solve for a+b | Math Olympiad Preparation

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Mathematical Olympiad | Solve for a+b | Math Olympiad Preparation

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[sardarji]

Very brilliant channel love from india

[philipkudrna]

Very impressive! Once again our professor has demonstrated that he is a real number artist, if not magician! Many techniques combined and a very satisfying result!

[Abby-hisf]

After 7999 = u^3 + 3u^2 + 3u, adding 1 was amazing trick

[sandanadurair]

I didnt get the clue of adding 1 and couldnt proceed further. Hahaha

[ravikumargautam]

sir, i have a problem in the following question, if sinA+sinB+sinC=0, cosA+cosB+cosC=0 then find the value of sin3A+sin3B+sin3C=?

[math]

great job, thanks so much for sharing

[SuperYoonHo]

thanks so much sir these help really a lot

[davidfromstow]

Excellent! I got as far as your first equation and then had to give up but loved your solution and explanation. Thank you

[anatoliy]

Nice task. And your math trick with substitution is also nice. Thank you so much, Mr PreMath. all the best to you and your family. Reykjavik Jazz 2022 has started yesterday. I don`t know if you like jazz but I nevertheless would like to invite you thither<))

[iitjeetobecracked]

Excellent way of approach, btw sir are you from India?

[mehulpunia]

Substitution is a beautiful ornament of mathematics

[prabhudasmandal]

Thanks for the trick. I did it this way. Multiplying partly the lhs of the 1st equn, it is (a+b) (a+b+ab+1) =2022. the 2nd equn is (a+b) ^3--3ab(a+b) =1933. Now substituting x for(a+b) and y for ab in both the equns we get x(x+y+1) =2022 Or x^2+xy+x=2022, say equn (A). and x^3--3xy=1933, say equn(B). Now, to eliminate the complex xy from both of them, multiplied (A) by 3 and got 3x^2+3xy+3x=6066.now, adding (A) and(B), got x^3+3x^2+3x=7999. Adding 1 to both sides, it is x^3+3x^2+3x+1=8000 or (x+1) ^3=(20) ^3 or x+1=20 or x=19.ans.

[XLatMaths]

I did it the same way but forgot to add 1 to make the cubic obvious. I knew 7999 was basically 20³ so I guessed 19 and it worked...need to practice the rigorous methodology more.

[giuseppemalaguti]

Ponendo s=a+b, sviluppo i dati e trovo una equazione cubica in s, s^3+3s^2+3s-7999=0, che da soluzione s=19, unica reale

[thomasrochow]

fantastic and clear solution; mavy thanks. but a=? b=?

[girolamocapita]

Very good, Easy but only you catch the right way.😄

[ralkadde]

I was curious what might be the solutions for particular a and b, despite this was not the question. And so: a = (+sqrt(5529)+361)/38, b = (-sqrt(5529)+361)/38, while a and b are interchangeable. Prove: a+b=19, a^3+b^3=1933, and (1+a)(1+b)(a+b)=2022. (Funny the complicated a and b lead to current year 2022.)

[rukaiyashukra]

Sir make a video about all kinda equations

[alster]

After seeing the

(u+1)³=8000

I figured it out and stopped the video and solved it on my own and got 19.



Fast forwarded to the end double check and it did match.

Keep it up and salute from the Philippines! 🇵🇭🇵🇭🇵🇭🇵🇭🇵🇭