A Nice Math Olympiad Algebra Problem. X=? & Y=?

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[@aliengaming_squad7579]

Wow you give us a simple problem with unexpected solution

[@loloflores123]

Substitution method: at the beginning, you solve below, x=50/y. You substitute this above. 50/y + y = 5, then 50 + y² = 5y, then y² - 5y + 50 = 0, you solve y, and then you solve x.

[@saidkibal5312]

Mais on a dans cette solution delta inférieure à 0

[@ahuiyigun3576]

While you were finding the solution I found x and y, made myself a Turkish coffee, had some M&Ms, loaded the dishwasher... Try using (x+y)²=5² and -(x²-y²) next time...

[@khanzee1387]

Excellent👏💯

[@learncommunolizer]

Thank you 🙌

[@anshichaudhary0156]

Shri dharacharya formula i think, one of my favourite

[@FrankStanley-j5y]

Straightforward High School math, although the solution given is overcomplicated.

[@jalex23]

You studied imaginary numbers in HS? That's quality education...

[@Pagokeraunos]

​@@jalex23Yes, in Greece we study imaginaries in depth, during the 3rd year of highschool. They are part of the Panhellenic exams to get into university. I don't know where the original commenter is from though.

[@jalex23]

@@Pagokeraunos impressive, in Mexico we see in HS, Algebra, Trigonometry and Calculus. Imaginary numbers are only for applied maths in college. I studied it in my second semester of engineering.

[@wyldeman7]

​@jalex23 I went to high school in a town with two stoplights and we had calculus. That was 25 years ago.

[@trancus11]

Wow that solution was totally unreal.

[@roberttunnicliffe3470]

i see what you did there.

[@UncannyPally]

Did you imagine it would work out that way?

[@thomaswopelka4682]

One could already imagine it's going to be an unreal solution.

[@saieshpethe8742]

Here in India quadratic equations are basic for me I studied this types of problems in 7th-8th grade

[@marimo_monster]

It’s basic 9th grade in Russia

[@natep1661]

I have no idea what's going on, but I'm glad you do.

[@ppd3bw]

A rectangle with the area 50 and sides a+b=5 does not exist. The rectangle (a+b=5) with the largest possible area (ab) is a square with a=b=2.5. Its area is 6.25.

[@erbol21]

This is an imaginary rectangle 😊

[@siarzukzarski3120]

-"Он сделался поэтом, потому что у него было слишком слабое воображение, чтобы быть математиком." ©

[@nicholasmenditto404]

Just like i said in high school. I have never needed to know how to do this.

[@kristir1262]

Commenting just because there are so many negative comments. This was straightforward and easy to follow. Good to review these now and again 👍

[@faytesaurelius350]

Uh, okay, so, the exact values of X and Y would be....? If we refer to these solutions, of course. By my own logic, you just have to search what's X and what's Y first. If X+Y = 5, what number added to Y would equal to 5, if you're considering the 2nd equation XY=50, be?

[@kristir1262]

​@@faytesaurelius350 and you would be right if we were only looking for real numbers. That's the whole point, there are other solutions in the complex set, where numbers have an imaginary part. Complex numbers are widely used in advanced math, engineering and physics.

[@deelust4208]

We are solving the system of equations: 1. \( x + y = 5 \) 2. \( xy = 50 \) ### Step 1: Solve for \( y \) in terms of \( x \) using the first equation From \( x + y = 5 \), we get: \[ y = 5 - x \] ### Step 2: Substitute \( y \) into the second equation Substitute \( y = 5 - x \) into \( xy = 50 \): \[ x(5 - x) = 50 \] Simplify: \[ 5x - x^2 = 50 \] Rearrange: \[ x^2 - 5x + 50 = 0 \] ### Step 3: Solve the quadratic equation The quadratic equation is: \[ x^2 - 5x + 50 = 0 \] Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1 \), \( b = -5 \), and \( c = 50 \). Substitute these values: \[ x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(50)}}{2(1)} \] \[ x = \frac{5 \pm \sqrt{25 - 200}}{2} \] \[ x = \frac{5 \pm \sqrt{-175}}{2} \] ### Step 4: Simplify Since the discriminant (\( -175 \)) is negative, the solutions are complex. Rewrite \( \sqrt{-175} \) as \( i\sqrt{175} \): \[ x = \frac{5 \pm i\sqrt{175}}{2} \] Simplify further: \[ x = \frac{5}{2} \pm \frac{i\sqrt{175}}{2} \] ### Step 5: Find \( y \) Using \( y = 5 - x \): \[ y = 5 - \left(\frac{5}{2} \pm \frac{i\sqrt{175}}{2} ight) \] \[ y = \frac{10}{2} - \frac{5}{2} \mp \frac{i\sqrt{175}}{2} \] \[ y = \frac{5}{2} \mp \frac{i\sqrt{175}}{2} \] ### Final Answer The solutions are: \[ x = \frac{5}{2} \pm \frac{i\sqrt{175}}{2}, \quad y = \frac{5}{2} \mp \frac{i\sqrt{175}}{2} \]

[@naukrisearch]

X^2-5X+50=0 x^2-10x+5x+50=0 (x-10) (x-5) X= 10 is correct Xy=50 Y = 5

[@darkreasondetre4156]

x = (5/2) - ((5 i root(7))/2); y = (5/2) + ((5 i root(7))/2)

[@wes9627]

Substitute x=5/2+z and y=5/2-z into the second equation: (5/2+z)(5/2-z)=50 or 25/4-z^2=50 This yields z^2=-175/4 or z=±i(5/2)√7. Thus x=5/2+z=(5/2)(1±i√7) and y=5/2-z=(5/2)(1∓i√7)

[@vladimironoprienko7177]

I square the first equation, subtract from the result the second equation multiplied by 4, get (x-y)=±√175i. Add and subtract the first equation to get 2x and 2y.

[@ВячеславСадонин]

Это более изящное решение чем тупая подстановка и решение квадратного уравнения.😊

[@poec3292]

Hard to believe they would force an imaginary number into math calculations rather than say that it is not possible.

[@davidburke2132]

Imaginary numbers are absolutely needed for applications in the real world. Just one example is in electrical engineering where imaginary numbers are used to analyse AC circuits, in particular the amplitude and phase of electrical oscillations. If maths had just decided “that’s impossible” with respect to imaginary numbers many of the things you take for granted in the world wouldn’t exist.

[@maruthimgowda8963]

Full length steps they do simple step

[@naukrisearch]

Solution has overcomplete, it's has simple solution

[@СиСе]

Обычное квадратное уравнение. Ну да комплексные числа. Но не олимпиадная задача

[@amm2019]

X = -5 , Y= -10

[@Aoeira]

Wow I didn't expect imaginary numbers to a high school olympiad. In my country they are taught just at the last senior high school grade (and they are considered the easy subject). For what grade is this olympiad? And I'm curious in what grade imaginary numbers are taught in this country? Also it was unexpected seeing straight up the X1, 2 solution and not separate the Δ=b^2-4ac - > Δ

[@ammaamma5480]

x+y=5 xy=50 5+0=0 50=50 So x=5. y=0. prablam salvd

[@НатальяТкаченко-ъ1з]

Если построить графики функций y=5-x и y=50÷x, то они не будут иметь точек пересечения.

[@АртС-ж2щ]

В стандартном виде корней нет. Но тут решили через комплексное число корни найти

[@WikoLite3172]

E = mc² 🙃

[@airstriked_247]

I understood half of it then I got lost at the end

[@strangexj86]

I love how they just used a letter to make impossible math solutions work. I love it though. Excited to go back to school for mechanical engineering.

[@adriannanditya]

GG!!

[@memoriesofold9591]

Simple problem with a complicated solution. 😂

[@Italianor01]

10+-5=5 10.-5=- 50

[@heinrich5758]

You make unreal problem

[@tomforsythe7024]

But there are no numbers which add up to five and multiply to 50. What am I missing?

[@LaBibliotecadeJose]

The solution is an imaginary number

[@tomforsythe7024]

@@LaBibliotecadeJose OK, now I get it.

[@andychisarick6879]

When I fantasize something it's not long convoluted math problems & imaginary numbers that I'm fantasizing about. Each to his own I guess​@@LaBibliotecadeJose

[@ribkahelindra8720]

Wow why i dont understand this when im on school back than Its look make sense now

[@arceligasol8170]

P2 + k2 !

[@zindeginamilegidubara1050]

My brain is totally gonee bro

[@MuhammadAlFateh-h1b]

How can be X + y = 5 ??? X+y probbalyy =XY

[@Haseena-yv9fl]

Too good love it❤

[@PandurangPeese]

when the question is for 20 marks

[@nuttaerez884]

Why i^2 = -1

[@jalex23]

Olympiad question at which grade? Seems like a normal excercise when studying imaginary algebra.

[@Smith1000R]

How to make a simple task into a complex one... No real number solution

[@luigicorvi1661]

X IS 5 Y IS 0

[@oreorobot2624]

Olympiad really? It's simple problem for me.

[@Hasanbasri-sj3py]

y=5-x x.y=x.(5-x) [(5x-x²)]’=5-2x=0 5=2x x=5/2 y=20 x=5/2 y=5/2 fu*k

[@manishvidhya6778]

😮😅😂😂😂😂

[@kd8opi]

Glad I got it on the first go.

[@preyzcruz]

This is one of those ok so whats the answer

[@Mrpanishev]

Вот, ну и где ты практически применишь этот результат!!!?

[@ramkp8763]

Thanks for your steps sir

[@HypnoticPhantom]

Algebra, the most convoluted way to reach an answer.

[@kirezarzev5788]

X = -5 Y = -10 😊

[@BulletSponge178]

Then x+y would equal -15, genius.

[@olafbernhards]

-5 + -10 is -15 you fail

[@louisthomasic275]

Solutions of x^2-Sx+P=0 I learnt this when I was 15...

[@The-spice-lover]

It's simple! X = 5, Y = 0 X + Y = 5 XY = 50 Solved!

[@igorgrigorov4858]

Любое число умноженное на ноль равно ноль. Обратно в школу

[@Lord-Andre]

Ääääh……..no 😁🧙‍♂️😁

[@bryanlas]

Riiiighhttt....

[@faytesaurelius350]

Uh, Y=10. X=-5

[@chadf86]

​@@faytesaurelius350 that would also be wrong. There is no correct answer.

[@ptaaungthitsar6892]

တဆယ် ငါးလီ ငါးဆယ် တဆယ်အပေါင်း အနှုတ်ငါး ညီမချက်းငါး

[@debdattachatterjee1]

What is ova

[@marceliusmartirosianas6104]

x+y=5 xy=50]=[[[ xy= 10^5=5 xy=5 1)xy=5 xy-yx=5-5]=1=1]=[ xy=1 xy=1 x-x=1=y [ trivialiai y=1

[@riyabawa5382]

#MathHelpers

[@EvgenS8]

Вместо 5 должно быть й

[@โนเซอร์นอยเซอร์]

10 and -5

[@faytesaurelius350]

I dunno. The first thing I say when I see the first and 2nd equation, I immediately state that X=-5, and Y=10, or vice versa. Spontaneously. But if we follow the solutions, what would the exact values of X and Y be here?

[@SimoneSaviolo]

Can't be: your xy would be -50.

[@tirtawang2503]

Wasting time

[@agampungo3511]

Indian any chance?

[@tinodejong6298]

Simple.... X = 5 Y = 0 XY = 50 5(X) + 0(Y) = 5

[@ТимурГараев-й7л]

Реально? Обычное квадратичное уравнение это задача на Олимпиаду? Индусы настолько отупели?

[@MrKotyanskiy]

Видимо, да, раз он после отрицательного корня начал пытаться дальше решить эту систему.

[@gomatimahadevan3265]

Why are you demeaning communities ? Don’t be racist

[@MrKotyanskiy]

@@gomatimahadevan3265 Bro, this is just a joke, it's clear that not all Indians are stupid, but the author of the video is really stupid. He is trying to seem smart, although halfway through the video one could understand that this equation has no solutions.

[@allailina1941]

​@@gomatimahadevan3265 индусы это теперь отдельная раса? Словарик купите для определения расизма

[@SirinimalDharmarathna]

x+y =5, xy =50 x.x --2xy+y.y =.25 -200 (x--y) = 5 root(-7)

[@shawnhutchings5931]

Seriously??? That’s like saying a turtle’s made up of x + y or xy = turtle. Try getting out once in a while, there is a world out there that’s made up of a whole lot more than x’s and y’s! But I’m sure posting videos like this gives your existence meaning. Bravo!

[@slshusker]

There were 48 people on the train when it left the station.

[@aether-vega]

No it no solution😂

[@digdougedy]

I'm going to stick my neck out and say that there is no solution where the two equations use the same numbers. x+y =5 and x multiplied by y =50 is not a logical question and does not have an answer. As for the algebra. I refer to Billy Conolly.

[@riyabawa5382]

#MathHelpers

[@bradevans5566]

It does have an answer; it was demonstrated in the exercise. It involves imaginary numbers, which is what is throwing you off I think.

[@digdougedy]

@@bradevans5566 What is throwing me off is that any numbers that added together equal 5 must include 2 numbers less than 5. Any equation where 2 numbers multiplied together equal 50 requires 2 numbers, one of which must be greater than or equal to 5. So it could be 1 x 50 or 2 x 25, ( can't have 3 unless we use a fraction 16 one 2/ 3rds.... 4 x 12.5. etc. The confused one is the guy who believes this is possible.. It isn't.

[@AkariKurosaki]

​@@digdougedy It is possible with complex numbers, the imaginary number was created to solve this type of problem.

[@నేనునేనే]

A classic algebra problem! Given: 1. X + Y = 5 2. XY = 50 We need to find X and Y. Step 1: Express Y in terms of X from equation (1): Y = 5 - X Step 2: Substitute Y into equation (2): X(5 - X) = 50 Step 3: Expand and simplify: 5X - X² = 50 Step 4: Rearrange to form a quadratic equation: X² - 5X + 50 = 0 Step 5: Factor or use the quadratic formula: (X - 10)(X + 5) = 0 Solving for X: X = 10 or X = -5 Now, find Y using Y = 5 - X: If X = 10, Y = -5 If X = -5, Y = 10 So, the solutions are: (X, Y) = (10, -5) or (-5, 10)

[@Valsionhezter]

XY=50. You didn't find what's wrong?

[@ioannisimansola7115]

I did it at school when I was 16 yo. Nothing important

[@myaman3579]

easy

[@Pmak]

x=5 y=0 5 + 0 =5 50 = 50. Easy.

[@Lonewolf-q6i]

Anything multipled with 0 is 0 so...xy = 0.. According to your logic

[@Pmak]

@@Lonewolf-q6i Bro, it's a joke if you just put 5 and 0 together it's just 50.

[@faytesaurelius350]

X is -5, Y is 10. Et voilà, problem solved. Easy math, grade school if not kindergartner level.

[@Lonewolf-q6i]

@@faytesaurelius350 Then xy = - 50

[@cookeatliverepeat8815]

Boring AF dunno why YT tortures me with so called " Math Problems"

[@tanyashively3980]

Nothing like going around your nose to get to your butt.

[@알쓰-k2z]

이런 영상들 보면 진짜 성의 없움 적어도 두 군의 합을 짝수로 하는 성의도 없움 그럼 분수 나오는거 뻔한건데, 설사 처음에 몰랐다고 해도 결과를 보면 아 좀 바꿔야 겠다하는 의지도 없눈게 웃김 ㅋㅋ

[@user-yn2sv9rm8n]

didn't say real solution. it's a complex solution

[@ngocdo5687]

- Olympiad ? XY = 50 , X + Y = 5 . Easy : XY = 50 = 1 x 50 = 2 x 25 = 5 x 10. 10 - 5 = 5 = X+ Y . X = 10 , Y = 5 .

[@LaBibliotecadeJose]

10+5=15 not 5. You have missed the whole point!

[@ngocdo5687]

@@LaBibliotecadeJose - Đây là Toán Thông Minh, không phải toán thông thường.

[@LaBibliotecadeJose]

@@ngocdo5687 ok! 🤷‍♂️

[@ngocdo5687]

@@LaBibliotecadeJose - I' m 72 yo Vietnam, and you ?

[@LaBibliotecadeJose]

@@ngocdo5687 Spain

[@sashabeloi89]

There is no answer

[@eurowebs]

X = 5 Y = 0 :-)

[@henryshepherd1050]

This explanation is so ponderous and repetitive

[@BrianONEILL-qf2cs]

So many of these ' Guy who sounds like Andy Kaufman in 'Taxi' solves one problem in 15 minutes' videos are nothing but 'mathturbation'.

[@katieevans6017]

well he goes through it, step by step, so everyone can follow. You might be looking for more advanced math where he skips the obvious.

[@indiandrtrust]

Your question is wrong.

[@asev1969]

Why do you think so?

[@deden77720]

cmon, like an idiom: “dont break your calculator if you dont understand.” “dont splash the water in front of you if you are ugly” 😂

[@moebiusfan9545]

​@@deden77720 I guess that doesn't translate into English very well.

[@MarioCindric]

12 min video for something which literally is solved in 1,5 minute.