Can You Solve the Olympiad Question? | Learn how to solve for xy quickly | Math Olympiad Preparation

[@Dr_Srinivasa_ramanujan]

sir it is nice question with awesome solution and I haven't seen this type of solution earlier so thank you so much Sir🤗❤❤

[@PreMath]

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

[@jasimmathsandphysics]

This channel has helped me so much that I’m able to do this in my head very fast and still get it correct. Thank you Pre Math!

[@PreMath]

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

[@jasimmathsandphysics]

@@PreMath thanks man

[@KAvi_YA666]

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

[@PreMath]

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

[@KashabGoshami969798]

Excellent

[@PreMath]

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

[@luigipirandello5919]

Very nice question and solution.

[@PreMath]

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

[@sandanadurair5862]

It is a real pleasure and fun to do such simple but tricky manipulations. I too got 25 thru another route. Continue to give us more such problems to keep our mind active. Thank you.

[@hussainfawzer]

I would love to know your method

[@sandanadurair5862]

@@hussainfawzer Hi Fawzer I rewrote first eqn as (x+y)^2-xy=119.......3 Squared second as (x+y)^2+xy-2(7+√(xy))√(xy)=49 (x+y)^2-xy-14√(xy)=49 119-49 = 14 √(xy) √(xy)=5. I made unnecessary rewriting and substitutions . Prof has done it neatly. I didnt try any novel approach. Thank you for your curiosity. My best wishes to you Fawzer Sandanadurai India

[@hussainfawzer]

@@sandanadurair5862 Thank you for the reply

[@PreMath]

Super, Sandanadurai! Thank you for your wonderful feedback! Cheers! You are awesome. Keep it up 😀 Love and prayers from the USA!

[@davidfromstow]

Superb, as always. Thank you

[@PreMath]

Our pleasure! Thank you for your wonderful feedback! Cheers! You are awesome, David 😀

[@242math]

you did an excellent job bro, thanks for sharing

[@PreMath]

Super! Thank you for your feedback! Cheers! You are awesome, my dear friend 😀

[@Trr1fstud]

I couldn't believe pre math make this giant so simple

[@PreMath]

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

[@sankhajitdas3220]

*pre math😶

[@pranaykumar5683]

Nice solution

[@alster724]

Very easy Olympiad Math problem. Got it in less than a minute.

[@PreMath]

Super, Kevin Thank you for your feedback! Cheers! You are awesome. Keep it up 😀

[@WSCLIVE786]

good effort

[@PreMath]

Glad to hear that! Thank you for your feedback! Cheers! You are awesome, my dear friend. Stay blessed 😀

[@HappyFamilyOnline]

Very interesting 👍 Thank you so much for sharing😊😊

[@PreMath]

Thanks for visiting Thank you for your feedback! Cheers! You are awesome 😀

[@mahalakshmiganapathy6455]

Thank you

[@PreMath]

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

[@ganeshdas3174]

Square the second condition and put values after fitting substitution ✓ xy = 5 on squaring it yields 25 as ans

[@ankurdwivedi4534]

Done took 10-12 minutes mentally👍👍😊amazing problem

[@PreMath]

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

[@SAURAVSINGH-gb2lw]

Similar channel for physics and chemistry???

[@PreMath]

Not yet! Stay tuned. Thanks for asking. Cheers! You are awesome, Saurav 😀

[@nicogehren6566]

nice job

[@PreMath]

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

[@nirupamasingh2948]

V nice v systematically solved

[@PreMath]

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

[@pranavamali05]

Thnku

[@PreMath]

You are very welcome. Thank you for your feedback! Cheers! You are awesome, Pranav 😀

[@markphc99]

This seems an easy to wrangle problem , I wonder what age group are these Olympiad questions are aimed at?

[@Skank_and_Gutterboy]

I took a different approach from the vid. I rearranged the 2nd equation to sqrt(xy) = x + y - 7, then squared both sides and expanded to get: xy = x^2 + 2xy - 14x + y^2 - 14y + 49. I then rearranged the first equation to: xy = 119 - x^2 - y^2. Now add these two equations. x^2, y^2, and xy terms cancel out and after some simplification you get: x + y = 12. Now use this in the 2nd equation to eliminate x + y and the result is: 12 - sqrt(xy) = 7. sqrt(xy) = 5, therefore xy = 25.

[@PreMath]

Great suggestion. Good job Thank you for your feedback! Cheers! You are awesome. Keep rocking 😀

[@illyriumus2938]

Same here 😀

[@anatoliy3323]

Thank you for an interesting task, sir! Functions like F (x, y) = 0 are called implicit functions, right? All the best to you

[@PreMath]

Dear Anatoliy, an implicit function is defined as a function with multiple variables. That is, one of the variables is a function of the other set of variables. A function f(x, y) = 0 such that it is a function of x, y, expressed as an equation with the variables on one side, and equal to zero. Thank you for your great feedback! Cheers! You are awesome. Keep it up 😀 Love and prayers from the USA! Stay Safe!

[@prossvay8744]

(x+y)^2=(√xy+7)^2 x^2+2xy+y2=xy+49+14√xy But: x^2+xy+y^2=119 119+xy=xy+49+14√xy 14√xy=119-49 (14√xy)^2=70^2 196xy=4900 xy=4900/196=25 So : xy=25

[@AmitKumar-xs7md]

Sir please tell us where did you get these types of question (which book) ? please text down below.

[@PreMath]

Dear Amit, we don not use any book. We just contact various institutions for that. I wish I could tell you any such book. Thanks for asking. Just keep watching PreMath channel. Cheers! You are awesome 😀

[@loveyall1910]

Can you help me with this question plz: a+b=1, a and b are real numbers, a,b>0, find the smalles value of P = sqrt(a(b+1))+sqrt(b(a+1))

[@srividhyamoorthy761]

thanks , the solution was clean with nice explanation, i knew the answer any average 8th grader could do this and of course i would have solved it and i watched it because you would get some watch time :)

[@marschallkenobi6426]

It's an easy problem but I don't think any average 8th grader could get it right, at least not in my country

[@PreMath]

Glad you think so. You are the best Moorthy dear. We are so proud of you. Thank you for your feedback! Cheers! You are awesome. Keep it up 😀 Love and prayers from the USA!

[@srividhyamoorthy761]

@@marschallkenobi6426 which country I am india and inknow all square and cube identities to soolve this

[@pranaykumar5683]

👌👌👌👌👌👌👌👌👌👌👌

[@broytingaravsol]

easy one

[@PreMath]

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

[@bekkarghezal6173]

permit me professor to suggest another way to solve these equation: x²+xy+y²=119 => (x+y)²-xy=119 => xy=(x+y)²-119 and (x+y)²-xy=(x+y)²-sqrt(xy)² => (x+y-sqrt(xy))(x+y+sqrt(xy))=77 =>(x+y+sqrt(xy))=17 given eq : (x+y-sqrt(xy)=7 means : (x+y)=24/2=12 so xy=(x+y)²-119=144-119=25

[@fatemakagzi4500]

Alternative method : Let's take equation 1 (X^2+2xy+y^2)-xy=119 (x+y)^2-(√xy)^2=119 (x+y+√xy)(x+y-√xy)=119 From equation 2 X+y-√xy= 7 Plugging value from eq 2 in eq 1 7(x+y+√xy)=119 x+y+√xy=17 x+y-√xy=7 Adding both eq x+y=12 12-7=√xy xy = 5^2 Xy 25

[@PreMath]

Super, Fatema Thank you for your feedback! Cheers! You are awesome 😀 Love and prayers from the USA!

[@devondevon4366]

Use a different approach x-sqrt(xy) + y=7 hence equation 1 x+y-7= sqrt (xy) let square hence x^2 + y^2 +49 +2xy-14x -14y=xy equation 3 Since x^2+ xy+y^2=119 then -x^2-y^2+119 = xy equation 5 let add equation 3 and 5 which gives 168 +2xy-14x-14y=2xy hence 168 -14x-14y=0 hence 168 = 14(x+y) 12 = x+y =12 equation 9 let's substitute equation 9 into equation 1, hence 12 -sqrt(xy)=7 12-7 = sqrt xy 5 = sqrt xy (5)(5)=xy 25 = xy Answer

[@Copernicusfreud]

That is exactly how I did the solution. I came up with x + y = 12, and plugged 12 into x + y - sqrt(xy) = 7. Sqrt(xy) = 5, so c.f. = 25

[@PreMath]

Very smart approach! Super, Devon Thank you for your feedback! Cheers! You are awesome. Keep rocking 😀

[@tanvirmahmud461]

Applying a²-b² formula at no 1 equation could have made it easier to solve 😉

[@ranveeryadav176]

No need to squaring If x-√xy+y=7 Then X+√xy+7=17 By subtracting 2√xy=10 Then xy =25

[@PreMath]

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

[@PankajSingh-cr8hj]

119/7 = 17 xy = (17-7 |2)² = 25

[@PreMath]

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

[@arregull]

25

[@PreMath]

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

[@leorvlog1416]

mahina ako sa ganyang problem solving,medyo mahirap unawain sa una pero sa huli makukuha mo rin

[@AlfonsoNeilJimenezCasallas]

do you agree (xy)^(1/2) = +/- 5 for this question?

[@PreMath]

Normally that is the case! Thank you for your feedback! Cheers! You are awesome, Alfonso 😀

[@JSSTyger]

I came up with xy = 25.

[@PreMath]

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

[@devondevon4366]

xy=25

[@PreMath]

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

[@Teamstudy4595]

Ans : xy = 25. Very very very very very easy question

[@PreMath]

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

[@yzhang2008]

I used a slightly different way: (x + y - 7)^2 = xy

[@PreMath]

Many approaches possible! Great job Thank you for your feedback! Cheers! You are awesome, Zhang. Keep it up 😀

[@MinhNhat-iv6fs]

Zzzz i have an another solution more intelliger but im too lazy😅

[@thomakondaciu6417]

Xy=25

[@PreMath]

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