I get two more as the solns to x = +/- e^(ln(2)/4x) . The negative version has one soln, and the positive has another 2 more, of those 2, one is 16. x* = { -4 W(-ln(2)/4)/(ln(2)), -4 W(ln(2)/4)/(ln(2)), 16}
@GeriReshef29 күн бұрын
Why the solution is so complicated? X^3+X=130 X^3+X^1=5^3+5^1 /*did you find it by a chance?*/ X=5 2^n=5 n=Lg2(5)
@MARTINWERDER29 күн бұрын
@matholympiadonlinesolver 1/ 2 log base 5 = 5 log base 2 (= 2,321928) applied in the initial equation does not prove to be correct. x = 3 and - 0,430676 (= negative 0,430676) are correct solutions and they give the result 500.
@sunnysharma5166Ай бұрын
2005 is the answer,I solved it now
@matholympiadonlinesolver29 күн бұрын
🥰
@sunnysharma5166Ай бұрын
3/2
@matholympiadonlinesolver29 күн бұрын
🥰
@sunnysharma5166Ай бұрын
1/3
@matholympiadonlinesolver29 күн бұрын
🥰
@sunnysharma5166Ай бұрын
1/3
@matholympiadonlinesolver29 күн бұрын
🥰
@sunnysharma5166Ай бұрын
7! is the answer,solved in mind
@matholympiadonlinesolver29 күн бұрын
You are so clever
@armachamАй бұрын
You only found one solution, there are other real solutions
I will make vedio on the same problem thanks for the inspiration
@matholympiadonlinesolver2 ай бұрын
Yes, thank you, sir
@Ablee2 ай бұрын
Hello, I have noticed a problem. The thumbnail of the video shows a minus between the exponential numbers, but in the video you solve it with a plus.
@matholympiadonlinesolver2 ай бұрын
Ok thanks
@tejpalsingh3662 ай бұрын
Unnessory leanthy
@vannkan81522 ай бұрын
I like this solution. make more videos
@matholympiadonlinesolver2 ай бұрын
Thank
@vannkan81522 ай бұрын
Cool
@minxythemerciless3 ай бұрын
m = 2004 and n = 2005 are obvious solutions.
@mithunarora3 ай бұрын
4009 is the other trivial solution
@yodaami3 ай бұрын
What age Olympiad would that one be in? 60 yr old woman who did maths A level at school 40 years ago, feeling quite pleased to get this one easily.
@matholympiadonlinesolver3 ай бұрын
It is for the lower class.
@yodaami3 ай бұрын
@@matholympiadonlinesolver age? 7,8,9, 10, 11?
@matholympiadonlinesolver3 ай бұрын
@@yodaami yes it is for 10 years old
@nexio54543 ай бұрын
With small numbers like this, you can just list perfect squares under 45 and find by try and error. I solved it in 15 seconds like this :))
@MrRedEngineer3 ай бұрын
I agree. But I don't agree with that mention how fast you solve buddy. Lower your ego and accept his solution.
@nexio54543 ай бұрын
@@MrRedEngineer I accept his solution and it's definitely the most elegant solution. I didn't mean to show off and I'm sorry if my comment seems like I did. The problem being presented as an olympiad problem (which it clearly isn't), the goal would be to solve fast hence my solution and my exemple
@matholympiadonlinesolver3 ай бұрын
Thank you
@kiloperson56803 ай бұрын
Might I ask what country are you from?
@matholympiadonlinesolver3 ай бұрын
I'm from cambodia
@kiloperson56803 ай бұрын
@@matholympiadonlinesolver oh i asked because your pronunciation sounded like french to me haha, weird
@coderhub-tech79423 ай бұрын
Tried calculating based off the thumbnail, i got c²-a² = -5 so (c+a)(c-a) = -5, using that and a little brute force, the 4 possible values are c = ±2, a = ±3. From there you get b = ±6 which is the solution
@matholympiadonlinesolver3 ай бұрын
Ok thank you
@bledlbledlbledl3 ай бұрын
the way i went about it was very similar to that. looking at the thumbnail, a² must be 5 more than c². starting from 1 and just squaring a few numbers, it didn't take long to notice that 3² was 5 more then 2². from there, finding b² was just a subtract
@Abby-hi4sf3 ай бұрын
Always a+b > a-b , so you should not have four cases . I will assign the greater factor to the greater eqn
@coderhub-tech79423 ай бұрын
Does not apply if b is negative, think again
@Abby-hi4sf3 ай бұрын
@@coderhub-tech7942 Let us not forget that every negative number squared is always positive. All variable a, b, c, are sqared on the question So the answer is a= +/- 3 , b= +/- 6 and c= +/- 2
@coderhub-tech79423 ай бұрын
@@Abby-hi4sf true, but you are factoring a²-c² or c²-a² depending on your approach, which can include negative numbers, so your argument doesn't work there
@Abby-hi4sf3 ай бұрын
@@coderhub-tech7942 Whether you are factoring a²-c² or c²-a² , the fact remain that each variable is sqared .ex a²= (-a)² and (-c)² =c² so a²-c² = (-a)²-c² = a²-(-c)²
@honestadministrator3 ай бұрын
writing z for sin^2 ( x) one gets f ( x) = (1 - z + z^2) /( z + ( 1 - z) ^2) = (1 - z + z^2) /( 1 - z + z^2) = 1
@matholympiadonlinesolver3 ай бұрын
Nice
@vasilesinescu843 ай бұрын
How do you pronounce x?
@matholympiadonlinesolver3 ай бұрын
What are you hearing?
@quelquun56333 ай бұрын
One other way to see it is to know that sin^4 -cos^4= sin^2-cos^2. Then everything cancels out and you get the result.
You messed up the x part, you somehow made it into /2(sqrt(5)+2) instead of 2(sqrt(5)+4)
@jwkim44284 ай бұрын
derivative of f(x) is 0. f(x) is constant and f(0)=1. hence f (x)=1 for all x.
@matholympiadonlinesolver4 ай бұрын
Ok thank you
@davidsousaRJ3 ай бұрын
@jwkim4428 how did you get thsi result? It is very tedious to calculate this derivative by the quotient rule, and there is no obvious term cancellation in the final result.
@rishabhraj37494 ай бұрын
Bro.. Nice explanation
@matholympiadonlinesolver4 ай бұрын
Thank you
@princesmith92124 ай бұрын
So simple Well done
@matholympiadonlinesolver4 ай бұрын
Thank you
@laseriitd4 ай бұрын
first like
@matholympiadonlinesolver4 ай бұрын
Thank you sir❤
@Redstoner345264 ай бұрын
But arent there infinite solutions such as logbase2(10) for x and logbase3(3) for y or whatever other numbers you want that make 7