Olympiad Mathematics | Find all solutions | Math Olympiad Training

Can you solve the given math olympiad question involving cube and fourth root radicals?

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Olympiad Mathematics | Find all solutions | Math Olympiad Training

Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!

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[SuperYoonHo]

Thanks so much sir!!! That was an amazing question

[kwa]

After the first step, just raise both side to power of 12 is a little bit simpler.

[RichWoods]

I prefer to start off by getting bounds and simple solutions by inspection before doing any algebra. Here we can see that there are no negative solutions for x because a negative value can't have both a cubic and a quartic real root. Inspection also shows that x=0 is a valid solution, which removes the need to allow for it in the subsequent algebraic manipulation. Consequently it takes just five lines of algebra to reach the remaining solution for positive values, x=256/27.

[davidfromstow]

I got as far as your 2nd equation and then ground to a halt - thank you for the elegant solution.

[murdock]

Excellent task - marvelous solution, thank you 🙂. Remark: put all x-values on the left hand side and all the others on the right hand side makes the math quite a bit easier. Just raise both side to power of 12. And (256/27) = (16/3)²/3 😊. And obviously x = 0 is another solution.

[shahin]

❤️ this channel is really helpful thank u

[chitranshraunak]

I did it exponentially and eventually ended up with just one solution i.e.256/27and ate up 0.This solution helped me to always think of 0

[fabatcazityt]

Thanks so much Mr 🥰🥰🥰🥰🥰🥰 you are a legende🧑‍🏫🧑‍🏫🧑‍🏫

[mehulpunia]

Thank you so much sir for this explanation

[christianthomas]

just multiply by the conjugate so that we get: after some basic = (4^(1/3)/(3^(1/4))^2
and after some more divisions and exponentiations: x=(4^(4/3))^3 / 3^3 which gives us: x= 4^4 / 3^3 which is 256/27.

[reinamaeda]

Checking the solution for x=0 is easily done, but what about the other solution 256/27? I'd love to know how it works

[seegeeaye]

factorize the given equation as x^1/4(4^1/3 - 3^1/4(x^1/12)) = 0
from that we get x = 0 and x = 256/27

[zahari]

Just put the second term on the right side and take 12 power of both sides.

[gdtargetvn]

You can just raise both sides by 12 right away instead of dividing and then cross-multiplying.

[owlsmath]

Good one! I rushed to solve it quick and so i forgot about the x=0 solution. Sorry PreMath.

[hansschotterradler]

X=0 is the obvious answer. For the case x not equal to 0 you can simply divide both sides by x^(1/4) and solve for x.

[Sakshi__choubey]

Sir I can't understand the firs step please explain if you can 🙏

[Icewallocumm]

I didn't watch the vid yet but I think it will be interesting

[Rufilale]

X=0 doesn’t fit as a solution as I see