Mathematical Olympiad | Nice Algebra Problem | Math Olympiad Preparation

Can you solve the given rational problem? Find the value of Rational Expression (x/y)+(y/x) if
(x^2/y^2 )+(y^2/x^2 )=223

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Mathematical Olympiad | Nice Algebra Problem | Math Olympiad Preparation

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[anatoliy]

Ingeniously simple! Your tasks are good gymnastics for the mind and relaxation for the soul at the same time. Thank you so much, Professor! God bless you and your family!

[alster]

After seeing the 223+2, I knew it was +-15 all along.

That is indeed quick

[davidfromstow]

You always make it look so easy...!!! Thank you.

[paulc]

Thank you for the video. The equation (a+b)^2 = a^2 + b^2 + 2ab is a powerful solving hint.

[meldatv]

You make it look so easy. Thank you for sharing your mathematical genius.

[hassanmahdi]

اني استمتع كثيرا بطريقتك في حل المسائل.
شكرا جزيلا.

[govindashit]

Easy problem.
Good explanation.
Thanks sir.

[math]

love this algebra problem, you demonstrated the simple solution very well

[haikalmroyyan]

I show another solution let x²+y²=a and xy=b. x⁴+y⁴/(xy)² = 223 → (a²-2b²)/b² = 223 so a=15b. Then just subtitution to x/y + y/x → a/b= 15.

[sy]

I introduce another method.
At first, from the problem equation, we get x^4-223x^2*y^2+y^4=0. The left side can be (x^2+y^2)^2-225x^2*y^2=0. Therefore, (x^2+y^2)^2-(15xy)^2=0.
Factoring this equation gives: ∴ x^2+y^2=15xy or -15xy. And next, by "divided by xy (= not 0)", we get the solutions: x/y + y/x = 15 or -15.

[lifestylewithrukhsana]

Very informative video thanks for sharing

[RobG]

Your explanations are very helpful.

Two things that I find interesting which you'd explain well:

1. proof of the Pythagorean theorem shown in Edward Tufte's book The Visual Display of Quantitative Information

2. the method of multiplication called Russian peasant math or Egyptian math which involves doubling one number and halving the other

That second could serve as an introduction to binary math.

[Don't tell the Florida governor that some math is non-binary.]

[mathsdone]

As usual, brilliant explanation . Well done, sir 👍👍👍👍👍

[maxmayorov]

i was taught that a^2+b^2 is not the same as (a+b)^2. but we can see that: x^2/y^2=(x/y)^2 and y^2/x^2=(y/x)^2. it is exactly a^2+b^2. so the formula be like a^2+b^2=(a+b)^2 - 2ab. hence it follows that (x/y+y/x)^2- 2=223 and so on.

[remixs_apprentice]

Sir pls solve this question.. if 7sin^2theta+3cos^2theta=4, find tan theta without using any identity of trigonometry

[ramanivenkata]

Though a simple sum, wonderful working.

[АлександрИванов-фэя]

Благодаря Вам решил в уме. Большое спасибо.

[SuperYoonHo]

thank you from now on i will study with you'r videos and not mathbooks cause' u r the best
#yourock

[furzaanullah]

Thank you Sir. Love and Prayers from India.
By the way, what is your name

[realitybites]

15 - solved just by looking at the problem