Math problem for advanced students

What do you think about this question? If you're reading this ❤️. Have a great day!

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@higher_mathematics

#maths #math

[marleybone]

Lambert and nature lock? This has reached the level of absurdity.

[baselinesweb]

Cmon man. If you’re gonna do all that stuff, at least pick a problem that you can’t solve by looking at it for a second or two.

[shoutplenty]

7:27 lol nice try

if i can spot 2^11 = 8 * 2^8 then i can spot 2^3 + 3 = 11, it’s the exact same thing

[kuerzebap]

Im reellen Zahlenraum R für x fällt die einfachste Möglichkeit x=3 direkt ins Auge. Da sowohl f(x)=2^x und g(x)=x streng monoton wachsend sind, kann es keine weiteren Lösungen in R geben.

[Marinealver]

Whenever you see an exponential with a linear you know you need to use the substitution method.
Now figuring out what to substitute is the tricky part.

[Roarshark]

Very nice solution, Lambert W strikes again!

[lapichfamily]

Solution simple : 3 est solution évidente, 2^x+x est strictement croissante donc injective. Il y a ainsi au plus une solution. Comme on en a trouvé une, c'est la solution.

[Roarshark]

What I appreciate about this channel above others: (a) you spell out every step (b) you give practical advice on how to tackle the problem (c) clear and consistent speech with no visual distractions (d) VERY neat and proper handwriting. My requests: can you please also cover calculus, differential equations, linear algebra and discrete math?

[mayaq]

“And never never use Wolfram Alpha to obtain the right side value” 🙄

[bkkboy-cmeb]

2^x+x=11
x≡1(mod2) → x=2k+1 (k≧1)
2^(2k+1)=11-2k-1=2(5-k)
2^(2k)=5-k≧4 → k=1
∴x=3

[s.a.r.lcyclopharm]

When you decompose 11 into 3+8, you seem to know the solution, rather to use inspection, and after few videos, you are always enforcing W function to resolve equations!!

[pspandey]

1:03 .1=(11-×)2^-×
2^11=(11-×)2^11
=>2^3)(2^8)=(11-×).2^( 3:23
3:26 11-×)
=>w{8ln2.e^8ln2}
=W(11-×)ln2.e^(11-×)ln2}
=>8ln2=(11-×)ln2
=>8=11-×&×=11-8=3

[richardslater]

Most of your videos involve impossibly random steps that prove to be correct but are totally unintuitive. This video is a classic case of that. In an exam situation, your solution would take longer than the entire time allowed to figure out the randomness of this solution.

[peterreali]

The exposition above uses a lot of non obvious tricks to solve the problem with the Lambert function which most people have never heard of. How about using some basic logic without guessing:
so write 2^x +x = 2^y + y= 11 now a power of 2 must be less than 11 so it has to be y = 3 hence x =3.

[jamesbond_]

Is there a way to solve this w/o using the Lambert W function? It would be great if you could show solving it with the Lambert W and solving it without using it. Thanks for all you do!

[pentasquare]

Trial and error mothed while being slow _never fails_

[justinstephenson]

An answer is obvious, a child of 10 could work it out but proving that is the only solution is hard.

2^x +x =11 => 2^x=11-x

From that we can conclude that (a) x is an odd number because 2^x must always be an even number.; (b) x must be a positive number because if x was negative the right side of the equation would be greater than 11 and the left hand side would be some fraction of 2 which is not possible (c) the maximum value of 2^x<11 which means that (I am using integers values of x for simplicity) that x<4 because 2^4=16 which is greater than 11.

Therefore if x is an integer the only possible answers are x=1 or x=3 and x=1 does not work.

But the problem did not state that x had to be an integer.

[nikolayguzman]

Very clear as usually. Excellent explanation. 🖐

[thakurfamily]

Uhmmm actually....

2^x + x = 2^3 + 3
The 2nd part of the equation satisfies x... so x = 3

😐

[RealQinnMalloryu]

{2x+2x ➖ }+{x+x ➖ }= {4x^4+x^2}=4x^6 2^2x^3^2 1^1x^3^2 x^3^2 (x ➖ 3x+2).