A tricky math problem for 9th Graders | Can you solve?

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Higher Mathematics

Higher Mathematics

Күн бұрын

Пікірлер: 40
@NeveraDalmatica
@NeveraDalmatica 2 ай бұрын
That a ninth grader can solve this equation is just as likely as the same ninth grader being able to solve a partial differential equation.😄
@DanielSong39
@DanielSong39 2 ай бұрын
Looks like a math contest problem for ninth graders
@martifingers
@martifingers 2 ай бұрын
I suppose it depends on which part of the world?
@ShanuJain-o9c
@ShanuJain-o9c 2 ай бұрын
You r just like me.When i was in eight grade i read university level trigonometry, calculus, complex numbers, so on... By myself. This problem is easy asf for me.
@justinstephenson9360
@justinstephenson9360 2 ай бұрын
A step was missed. Once you get to 2^x=3 Take a natural log on both sides you get log2^x=log 3 Basic rule of logs is log a^b=b.log a =>log 2^x=x.log 2 substitute that back into the equation gives you x.log2=log 3 =>x=log 3/log 2 On basis it is a 9th grader question and therefore complex roots are unlikely to be asked for, once you get to y(y^2+1)=30 it is relatively easy to see that y=3 is one answer because the integer factors of 30 are 3,10 or 5,6 (or vice versa) and we know that y30 when y>=6. That does not mean it is the only answer hence the wonderful extra steps in the video
@sergenjamkepo6467
@sergenjamkepo6467 2 ай бұрын
Changement de variable u=2^x u^3 + u =30 (eq1) Solution évidente u=3 On divise (eq 1) par u-3 et on trouve une équation du second degré dont on trouve les racines, et ensuite on passe en log
@964tractorboy
@964tractorboy 2 ай бұрын
I really enjoy your solutions to these problems. Thanks for sharing.
@Gnowop3
@Gnowop3 2 ай бұрын
In the old days when there was no calculator, we use log (base 10) because we have to use a look up table. In 2024, we can get results from calculator of different bases. Therefore 2^x = 3 => x = log3(base 2) [by definition]. Just find the value of x directly from the calculator without doing log3/log2.
@Segalmed
@Segalmed 2 ай бұрын
8^x = (2^x)³ . Substitute a for 2^x => a³ + a = 30. That ones is easy to guess: a=3 (27+3=30). => 2^x = 3 => x*ln(2)=ln(3) => x= ln(3)/ln(2)
@firstname4337
@firstname4337 2 ай бұрын
so you watched the video just like everyone else
@Segalmed
@Segalmed 2 ай бұрын
@@firstname4337 nope
@SmartGuyz
@SmartGuyz 2 ай бұрын
(27+2=30) should be (27+3=30) in this case
@Segalmed
@Segalmed 2 ай бұрын
@@SmartGuyz Thank you!. I have corrected the typo now.
@muido6389
@muido6389 Ай бұрын
(8x+2x) 8+2=10×3 because 30÷3)=10 ×3=30 ) Or 8×)+2x)=10x equal 8+1=9+1(1x+1x=2+8=10×3=30) 10+20-20=10×2=20+10=30)
@engone6380
@engone6380 2 ай бұрын
I thought about the same. Substitute 2^x by a for example, then write as follow a^3+a=30 then a(a^2+1)=30= 3(3^2+1).... Then a eq 3, much easier
@lynk5902
@lynk5902 2 ай бұрын
So these tricks only work because the numbers are set up perfectly. Show me how to do this if it was 29 instead of 30.
@dinabandhusaha5520
@dinabandhusaha5520 2 ай бұрын
Thank you for this
@kpkjolso
@kpkjolso 12 күн бұрын
Should’nt 8^x + 2^x = 30 be the same as 10^x =30? 8^x +2^x equals 10^x right?
@AlejanroDelHierro
@AlejanroDelHierro 2 ай бұрын
Did I missed at 4:47 => y^3+y = 3^3+3 ? y = 3, x^2 = 3 => 8^x +3 = 30 => 8^x = 27 => x =~ 1.585
@jdcunnington
@jdcunnington 2 ай бұрын
I've forgotten something. At 6:02, how does the last (y-3) become 1? There's something I missed.
@himanshusekharsahoo7301
@himanshusekharsahoo7301 2 ай бұрын
He took (y-3) common.
@jdcunnington
@jdcunnington 2 ай бұрын
@@himanshusekharsahoo7301 - oh, of course.
@RAMPRASADLANDAGE
@RAMPRASADLANDAGE Ай бұрын
Make video on sat maths question (vote button)
@better_than_uNOOB
@better_than_uNOOB 2 ай бұрын
u make very good videos i am in 8th and love loearning from u
@rrraewr
@rrraewr 2 ай бұрын
Lol i guesstimated it at 1.6 because 8 to the power of 1.5 is 8*2+ less than 8, which nets you close to 24, so some has to be missing to reach 30 with the help of 2 to not entirely the power of 2, has to be a step above 1.5, meaning 1.6
@nathanw4018
@nathanw4018 2 ай бұрын
You could also graph both sides of the equation and have a close approximation in 60 seconds
@pennstatefan
@pennstatefan 2 ай бұрын
Take the natural log of both sides, ln( 8^x + 2^x) = ln30. One then has x*ln2 + xln8 = ln30. x = ln30/(ln2 + ln8).
@rosschristofferson6084
@rosschristofferson6084 2 ай бұрын
Error
@pennstatefan
@pennstatefan 2 ай бұрын
@@rosschristofferson6084 show me the error
@pennstatefan
@pennstatefan 2 ай бұрын
I didn't give the final solution. One then has xln2 + xln2^3 = ln2 + ln3 + ln5. One then has xln2 + 3xln2 = ln2 + ln3 + ln5.: 4xln2 =ln2 + ln3 + ln5. x = (ln2 + ln3 + ln5)/4ln2.
@yanssala2214
@yanssala2214 2 ай бұрын
X = ln 3 / ln 2 = 1,58496..... # irracional el truco es un cambio de variable u = 2^x que conduce a una ecuacion simple de tercer grado u^3+u=30 una de sus soluciones es u = 3. Luego aplicar propiedades de los logaritmos y listo. Xln2 = ln 3 y ya sabemos el final.
@Unbathed
@Unbathed 2 ай бұрын
(I was in ninth grade 56 years ago. ) I tried to find the answer here starting with 30 = 2^5 - 2^1 followed by … 2^2X + 2^(X-1) = 2^4 - 1 … and got nowhere. Thank you for the rescue
@RealQinnMalloryu4
@RealQinnMalloryu4 2 ай бұрын
8^3x+2^3x={24x^3+6x^3}=30x^6 24^6x^6 2^12^2^3x2^3 1^6^1^1x1^1 3^2x^1^1 3^2x(x ➖ 3x+2).
@engone6380
@engone6380 2 ай бұрын
I thought about the same. Substitute 2^x by a for example, then write as follow a^3+a=30 then a(a^2+1)=30= 3(3^2+1).... Then a eq 3, much easier
@richardl6751
@richardl6751 2 ай бұрын
@@engone6380 He's not actually doing anything.
@sunilramkarran7037
@sunilramkarran7037 2 ай бұрын
You have to talk more slow
@javabeanz8549
@javabeanz8549 2 ай бұрын
There's a Playback Speed option in the Settings, adjust it to be slower.
@JoeA1974
@JoeA1974 2 ай бұрын
You are not a very engaging teacher.. sorry, I like some other KZbin math channels but I found yours to be dull and uninteresting. Absolutely nothing personal..
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