This is a nice Olympiad algebraic question. The solution was obtained using the laws of indices or exponentials. #matholympiadproblem #matholympiad #maths #matholympiadquestions #matholympiadpreparation #algebra
Пікірлер: 30
@user-pk4nk1et9h29 күн бұрын
Very clear process but you need a bigger board so that you keep most of the work available.
@JJONLINEMATHSCLASSchannel29 күн бұрын
Yes, you are right. But the board is big enough, what I need is a better camera that will get the whole board. Thanks.
@johnstanley569229 күн бұрын
Could also use synthetic division: let g1=a + b - 1 (=0), g2=a^2 + b^2 - 2 (=0), g3= a^11 + b^11 =(?) 1st obtain p2(b) =remainder= (g2/g1) = 2b^2 - 2^b - 1 = 0 . (here use 'a' as independent to return function of 'b') 2nd step get remainder p10(b)= g3/g1. Only need coefficients: [11 -55 165 -330 462 -462 330 -165 55 -11 1] final step, compute remainder p10(b)/p2(b)= 989/32. Advantage? never need to obtain values of 'a' or 'b'.
@JJONLINEMATHSCLASSchannel28 күн бұрын
Thanks
@prime42329 күн бұрын
One can use other exponentials to get the result. It just takes more time. Its important to show students other possible ways to get the same result. For example, the sum of a exponent 2 +b exponent 2 to the fourth power!!
@JJONLINEMATHSCLASSchannel29 күн бұрын
Thanks but that will make the video to be too long
@eldoserenado45829 күн бұрын
Very good...
@JJONLINEMATHSCLASSchannel29 күн бұрын
Thanks
@wilfredy.pasile7022Ай бұрын
Best maths teacher!
@JJONLINEMATHSCLASSchannel29 күн бұрын
Thanks for the compliment
@BN-hy1nd29 күн бұрын
Yes, you got me riveted. Well done 👍🏿
@JJONLINEMATHSCLASSchannel29 күн бұрын
I'm glad!
@Honeyshaf26 күн бұрын
To easy method for understanding the concepts
@JJONLINEMATHSCLASSchannel26 күн бұрын
Welcome
@dbrovnievic22 күн бұрын
You are so beautiful and so smart and on top of that, you have such a good-mood.
@nasrullahhusnan228928 күн бұрын
Problem solving outline given: a+b=1 and a²+b²=2 Outline: Find ab through (a+b)²=a²+b²+2ab Find a³+b³ through (a+b)³=a³+b³+3ab(a+b) Find a⁹+b⁹ through (x³+y³)³ Find a¹¹+b¹¹ though (x⁹+y⁹)(x²+y²)
@JJONLINEMATHSCLASSchannel28 күн бұрын
Nice approach 🤝🤝
@golddddus27 күн бұрын
Accelerated Girard-Newton method: x^2-(a+b)x+ab=0 (Vieta). x^2-x-1/2=0 x^2=x+1/2 (1) S(k)=a^k+b^k (1)*x x^3=x^2+x/2 ⇒ S(3)=S(2)+S(1)/2=2+1/2=5/2. (1)*x^2 x^4=x^3+(x^2)/2 ⇒ S(4)=S(3)+S(2)/2=5/2+2/2= 7/2 (1)*x^3 x^5=x^4+(x^3)/2 ⇒ S(5)=S(4)+S(3)/2=7/2+5/4=19/4 (1)*x^4 x^6=x^5+(x^4)/2 ⇒ S(6)=S(5)+S(4)/2=19/4+7/4=13/2 Acceleration is your solution, direct multiplication, instead of boring calculation S(7), S(8), S(9) S(10). By the way x^2-x+abx^0 =0 ⇒ S(2)-S(1)+ abS(0)=0 S(0)=a^0+b^0=2 ab=-1/2😎
@girmamumicha164228 күн бұрын
please teach us from basics on derivatives
@JJONLINEMATHSCLASSchannel28 күн бұрын
Ok. Noted.
@MYeganeh10028 күн бұрын
👌
@JJONLINEMATHSCLASSchannel27 күн бұрын
Thanks
@wilfredy.pasile7022Ай бұрын
Genius lady indeed!
@JJONLINEMATHSCLASSchannel29 күн бұрын
Thanks
@JomilHussainBarbhuiya28 күн бұрын
Where are you from
@JJONLINEMATHSCLASSchannel28 күн бұрын
Nigeria
@JomilHussainBarbhuiya28 күн бұрын
Wow nice love from India
@augustopinochet684128 күн бұрын
If it is allowed to use the calculator, it can be solved within 5 minutes.