Mathematical Olympiad | Solve and Check the Radical Rational equation | Math Olympiad Training

[@FaixaPretanoENEM]

Calm and perfect step by step resolution, as usual. Thanks, professor!

[@PreMath]

You are very welcome. So nice of you. Thank you for your feedback! Cheers! You are awesome, CRMF 😀

[@dantallman5345]

Beautiful problem. It got under my skin and I spent way more time on it than I will ever admit. It’s remedial math time for a retiree. btw- The starting equations are a circle centered at 0,0 with radius sqrt(7) and and a cubic that looks roughly like a bell curve riding on a baseline y=-x. The two solutions are at the intersections of circle and bell.

[@fevengr9245]

Consistent with my talent for finding the more difficult approach: I set P=(x-6)/(x+10) and 1/P = (x+10)/(x-6). It took more time but I did finally get the correct answer. That was a clever problem!

[@PreMath]

Thank you for your nice feedback! Cheers! You are awesome. Keep it up 😀

[@jbreezy101]

Lol. But you got there

[@242bluewater9]

love this radical rational equation question, your step-by-step solution is awesome bro, 242 math here

[@PreMath]

Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀

[@ignacy7474]

Actually, youre my favourite channel on KZbin

[@waheisel]

Another way to solve is to let u=x+2 which gives sqrt((u-8)/(u+8)) etc. You end up with u=+or-17. I always look forward to the daily PreMath puzzle. Thanks!

[@PreMath]

You are very welcome. Keep watching Thank you for your feedback! Cheers! You are awesome, William 😀 Love and prayers from, Arizona, USA!

[@actions-speak]

I did the same substitution and the cancellation was very satisfying!

[@careerpk2904]

Your way of method is amazing

[@anatoliy3323]

Nice a task as always! I have solved it in the same way. Thank you, Professor! My congratulations on the Easter Holiday

[@PreMath]

May this Easter bring PEACE to Ukraine! Thank you for your feedback! Cheers! You are awesome, Anatoliy. Stay safe and blessed 😀 Love and prayers from the USA!

[@ManjulaMathew-wb3zn]

I like your method as always. Alternatively you could simply square both sides which will remove all radicals in one shot leaving a quadratic equation in terms of x right away. The two radiants being reciprocal s made the usually nasty middle term simply equal to two and made the rest of the numbers relatively smaller. Cheers!

[@pragnyaparamitadwibedy622]

Did this question with ease thank you sir

[@PreMath]

. Excellent! Glad to hear that! Thank you for your feedback! Cheers! You are awesome, Soumik 😀

[@predator1702]

Very nice solution👍. Thank you teacher 🙏.

[@PreMath]

You are very welcome. Glad to hear that! Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!

[@KAvi_YA666]

Thanks for video. Good luck sir!!!!!! Nicely and super!!!!!!!!!

[@PreMath]

You are very welcome. Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!

[@fouadhammout651]

Saraha ma3andich zhar la f tssahib la f zwaj walit tangoul tawahad maynawad tawahda Matahmal... '' '

[@mahalakshmiganapathy6455]

👌very nice explanation

[@242math]

very well done, thanks for sharing the solution to this radical rational equation

[@PreMath]

You are very welcome. So nice of you. Thank you for your feedback! Cheers! You are awesome, my dear friend 😀

[@divein2427]

this was very well explained, thanks for sharing bro

[@PreMath]

You are very welcome. So nice of you. Thank you for your feedback! Cheers! You are awesome, 242 😀

[@pranavamali05]

Thnku

[@PreMath]

You are very welcome. Thank you for your feedback! Cheers! You are awesome, Pranav 😀 Love and prayers from the USA!

[@sanaaarish7707]

Great Video!

[@PreMath]

Glad you enjoyed it Thank you for your feedback! Cheers! You are awesome, Sana dear 😀

[@SuperYoonHo]

perfect solution

[@marcelowanderleycorreia8876]

Professor, it is allowed to use calculator in such olympiad? By the way, congratulations for the resolution!!

[@nicogehren6566]

very nice question

[@PreMath]

So nice of you, Nico. Thank you for your feedback! Cheers! You are awesome 😀

[@fretan3950]

Another solution method would be to first square the equation, so that you have (x-6)/(x+10)+(x+10)/(x-6)+2=1156/225. This can then be simplified to 256/(x^2+4x-60)=256/225 so that x^2+4x-60=225 must be true. And that quadratic equation has the solutions x=15 and x=-19.

[@PreMath]

Great Thank you for your feedback! Cheers! You are awesome, Fretan 😀

[@prabhudasmandal6429]

Simple one. Thanks

[@vaibhavkrupakar240]

-19 won't make sense

[@xyz9250]

I did it by squaring both side of the original equation, and after simplification, arrived x^2 + 4x - 285 = 0, from there got the same final answers.

[@jim2376]

We want numerators and denominators that result in integer square roots. x = 15 works nicely since 15 + 10 = 25 and 15 - 6 = 9. That will give us (3/5) + (5/3). (9 + 25)/(5 x 3) = 34/15.

[@experimentingalgorithm1546]

Sir can you make a video on proof of why If ax^a = bx^b then a = b

[@PreMath]

Great question to ask! Pretty soon. Thank you for asking! Cheers! You are awesome 😀

[@SuperYoonHo]

thanks

[@mathfreak5702]

Yay! Got the same.

[@PreMath]

Bravo Glad to hear that! Thank you for your feedback! Cheers! You are awesome, Saitama. Keep rocking 😀

[@tuandanganh7603]

Before solving, you need to set conditions for the variable, then there is no need to retest the solution of the equation

[@umeshmyumi3519]

Nice 👍👍

[@PreMath]

So nice of you. Thank you for your feedback! Cheers! You are awesome, Umesh 😀 Love and prayers from the USA!

[@buff9943]

Спасибо за видео

[@j.r.1210]

This equation also can be solved pretty quickly without a substitution. Just work through the algebra directly, eliminating the radicals, to end up with a huge but fun quadratic equation: 256x^2 + 1024x - 72960 = 0. This reduces to x^2 + 4x - 285 = 0, which is easy to factor as (x + 19)(x - 15).

[@PreMath]

Great Thank you for your feedback! Cheers! You are awesome, JR 😀

[@susennath6035]

Thanks for ur reply. I definitely inform you as per your later example

[@nirupamasingh2948]

V nice

[@PreMath]

So nice of you. Thank you for your feedback! Cheers! You are awesome, Niru 😀

[@zplusacademy5718]

Very nice and beautiful ❤️

[@kikiadewardani824]

jos temenan...

[@broytingaravsol]

easy one

[@PreMath]

Super Thank you for your feedback! Cheers! You are awesome 😀

[@sparshraj1367]

I got it right ....😁

[@PreMath]

Excellent! Thank you for your feedback! Cheers! You are awesome, Raj 😀

[@gouravsaini6928]

Please solve this problem- 5^x + 2^x = 5

[@mdshikothossen284]

From Bangladesh

[@ranveeryadav176]

15 by value putting method

[@mathswan1607]

x=15 or x=-19

[@PreMath]

Excellent! Thank you for your feedback! Cheers! You are awesome 😀

[@Teamstudy4595]

Ans : x = 15. (*Easiest question )

[@devondevon4366]

and -19 as well

[@olgakornak3969]

9×25=225.

[@open_mind5465]

😭 I spent an hour trying and things scattered. In the end, I found that the solution is very simple 😐

[@susennath6035]

Sometimes you r giving long sum rather than IQ based sum . I hope ,you will prefer IQ based sum more rather than this type of monotonous sum

[@PreMath]

Dear Susen, please give an example to make this problem into an IQ based sum. Just want to see the glimpse! Thank you for your feedback! Cheers!

[@olgakornak3969]

34÷15=2.266666666666666666667.

[@olgakornak3969]

g=1 giorno?

[@victorfildshtein]

In the Soviet school, we were taught that it is necessary to determine the range of acceptable values. Here: (x-6)/(x+10)⩾0 ⇒ [(x-6)⩾0 AND (x+10) ⩾0] OR [(x-6)⩽0 AND (x+10)⩽0] ⇒ x⩽-10 OR x⩾6

[@giuseppemalaguti435]

19,-15.....ho sbagliato e' -19,15