Learn how to solve Olympiad Question quickly! | Solve for ab | Math Olympiad Preparation

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Can you find the product of a and b in the given system of equations? Step-by-step tutorial by PreMath.com
Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!
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9 апр 2022

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Комментарии : 108

@nirupamasingh2948 2 года назад

V nice and v systematically solved

@PreMath 2 года назад

Glad you think so! Thank you Niru! Cheers! 😀 You are awesome. Keep it up 👍

@jmcargal 2 года назад

Divide the left by the right. a^2 + ab + b^2 = 3. Square the right: a^2 -2ab + b^2 = 81. Subtract one from the other: -3ab = 78.

@think_logically_ Год назад

So did I. I believe, that's how it was supposed to be solved.

@Copernicusfreud 2 года назад

yay, I solved it. I used the formula of (a-b) ^3 = a^3 - b^3 - 3ab(a-b), which is a better fit for the problem. It was a very easy "plug-and-chug" with that formula. ab has an easy plug, and (a ^3 - b^3) is also an easy plug.

@Copernicusfreud 2 года назад

well (a -b) has the easy plug is what I meant.

@drdiegocolombo 2 года назад

I love it!

@PreMath 2 года назад

Super job Mark Thank you for sharing! Cheers! 😀 You are awesome. Keep it up 👍

@jbreezy101 2 года назад

I'd have used yours mark

@HappyFamilyOnline 2 года назад

Very interesting question👍 Thanks for sharing🎉🎉

@anatoliy3323 2 года назад

Nice a task and detailed explanation! Thank you so much, sir! Your tasks are just a pleasure! God bless you!

@PreMath 2 года назад

So nice of you Anatoliy You are very welcome. Thank you! You are the best. Keep it up 👍 Love and prayers from the USA!

@SladeMacGregor 2 года назад

Love it! Thanks!

@PreMath 2 года назад

Glad you think so! You are very welcome.! Thank you! Cheers! 😀 You are awesome. Keep it up 👍 Love and prayers from the USA!

@guyhoghton399 2 года назад

Simpler to use the identity (a - b)³ = a³ - b³ - 3ab(a - b).

@PreMath 2 года назад

Good tip Thank you! Cheers! 😀 You are awesome Guy. Keep it up 👍

@srividhyamoorthy761 2 года назад

Right I also that the same but whoever is making these videos must get some watch time and that's why I watched the vid

@giovannigino3675 2 года назад

I solved it the same way .

@ankeshpritam3409 2 года назад

Well explained 👏🏻👏🏻👏🏻

@pranaykumar5683 2 года назад

Nice solution

@RashmisABCD 2 года назад

Beautiful upload, nicely done and shown in your video, tanks for sharing, have a wonderful day, lk311

@PreMath 2 года назад

Thanks for visiting You are very welcome. Cheers! 😀 You are awesome Rashmi. Keep it up 👍

@eatmadtaha8381 2 года назад

Thanks

@fevengr9245 2 года назад

Well, I discovered the hardest way to solve this. I ground through the equations and ended up with B^2 + 9B + 26 = 0. Solving with the quadratic formula results in B = -4.5+2.398i. This results in A = 4.5+2.398i. Thus AB = -26. So, that’s how you solve the problem slowly.

@PreMath 2 года назад

Thank you for sharing! Cheers! 😀 You are awesome. Keep it up 👍

@e-e_-lw6ch 2 года назад

I solved this question like you but you have finished this question with equation when you find b^2 + 9b + 26. So b^2+9b= -26. a-b=9, so a=b+9. Finally,(b+9). b= b^2+9b which is equal to -26. Likely you tried the formula discriminant but without any transformation you can find reponse

@pranaykumar5683 2 года назад

Nice question

@thinhnguyenhuu6150 2 года назад

There's another way to solve: We have: (a - b)^3 = a^3 - 3a^2b + 3 ab^2 - b^3 So: a^3 - b^3 = (a - b)^3 + 3a^2b - 3ab^2 = (a - b)^3 + 3ab(a - b) Therefore: 27 = 9^3 + 3ab*9 27ab = -702 ab = -26

@PreMath 2 года назад

Super job Thinh Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@pragyanpratim1696 2 года назад

Thanks sir for the question. It was simple but your explanation is so good

@PreMath 2 года назад

Glad you think so! You are very welcome. Thank you! Cheers! 😀 You are awesome Pratim. Keep it up 👍 Love and prayers from the USA!

@owlsmath 2 года назад

Thanks! Good explanation. And good problem.

@PreMath 2 года назад

Glad you think so! You are very welcome. Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@user-wt6oe8nm7y 2 года назад

nice one and east one

@ROCCOANDROXY 2 года назад

As an extension of the above problem consider the following: Find all real pairs (a,b) and the restriction on y that satisfies: (a^3 - b^3 = y^3) and (a - b = y^2). After working it out we have: Let a1(y) = (3y^2 + sqrt(3y(4 - y^3)))/6 and b1(y) = (-3y^2 + sqrt(3y(4 - y^3)))/6 and a2(y) = (3y^2 - sqrt(3y(4 - y^3)))/6 and b2(y) = (-3y^2 - sqrt(3y(4 - y^3)))/6 where (0

@brunococchietto7496 2 года назад

At 12.30 in the morning is not the best time to solve maths problems, however the substitution method was not the way to solve it.So started again using the cube root and square root formulas and so I solved it.Never again at this hour again.

@pranavamali05 2 года назад

Thnku

@PreMath 2 года назад

You are very welcome Pranav. Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@SuperYoonHo 2 года назад

very nice

@govindashit6524 2 года назад

Simple problem. But explanation is awesome.

@PreMath 2 года назад

Thanks for liking Glad to hear that! Cheers! 😀 You are awesome Govinda. Keep it up 👍

@hansschotterradler3772 2 года назад

I was able to solve thanks to watching this channel!

@PreMath 2 года назад

Great job! Glad you think so! Thank you! Cheers! 😀 You are awesome Hans. Keep it up 👍

@GreatnessStrikes 5 месяцев назад

Very nice solution. I first found the solution of a²+b² We know that a²+b² = (a-b)² +2ab We also know that a-b = 9 Substituting the equation , 9² + 2ab = 81 + 2ab Therefore , a²+b² = 81+2ab We know that , a³-b³ = (a-b) (a2+ab+b²) and a³-b³ = 27 Therefore , a³-b³ = 27 (a-b) (a²+ab+b²) = 27 9 (a²+ab+b²) = 27 a²+ab+b² = 27÷9 a² + ab + b² = 3 a²+b² = 3-ab As a²+b² = 81-2ab 81-2ab = 3- ab ab+2ab = 3-81 3ab = -78 ab = -78÷3 = -26

@snekadurga8547 2 года назад

Thank you

@PreMath 2 года назад

You are very welcome. Thank you Sneka! Cheers! 😀 You are awesome. Keep it up 👍

@scandyland3807 2 года назад

I solved by cubing both sides of equation 2 and then substituting values

@Retroskiii 2 года назад

where did you get the 2 and the 3 from to make -2ab + 3ab ( I’m no longer taking algebra, this vid just popped up in my recommended 😂)

@fouadhammout651 2 года назад

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

@Infinium 2 года назад

Really nice video!

@PreMath 2 года назад

Glad to hear that! Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@NarendraKumar-hs1ce 2 года назад

Solved very very easily

@PreMath 2 года назад

Excellent Kumar! Glad to hear that! Cheers! 😀 You are awesome. Keep it up 👍

@parikshitparekh9903 2 года назад

Thanks again for a new rule :)

@PreMath 2 года назад

You are very welcome. Glad to hear that! Thank you! Cheers! 😀 You are awesome Parekh dear. Keep it up 👍 Love and prayers from the USA!

@pranaykumar5683 2 года назад

👌👌👌👌👌👌👌👌

@mahalakshmiganapathy6455 2 года назад

Easy problem nice explanation 🙂

@PreMath 2 года назад

Glad to hear that! Thank you! Cheers! 😀 You are awesome Mahalakshmi. Keep it up 👍

@srividhyamoorthy761 2 года назад

Yayyeyeyeyeye

@sigmamaleslogokijalegi6683 2 года назад

Nice one Sir

@PreMath 2 года назад

Glad you think so! Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@manualrepair 2 года назад

👍

@PreMath 2 года назад

Great Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@montynorth3009 2 года назад

I was interested to use the answer that ab = -26 in order to calculate the values of a & b. We are told that a - b = 9 Therefore b = a - 9 Substituting for b in the answer ab = -26 We get a (a - 9 ) = -26. Not solvable, but worth a try.

@PreMath 2 года назад

Thank you sharing! Cheers! 😀 You are awesome Monty. Keep it up 👍

@rachelelizabethmason18 8 месяцев назад

This is what was getting me! I could get to the -26 (once I was reminded of how to to the algebra hahah) but I have been used to using the “key” I was given to check my work and I couldn’t come up with any two numbers that multiplied to become -26 but could be subtracted to be 9 😭

@mathlover6169 2 года назад

Awesome

@PreMath 2 года назад

Glad to hear that! Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@mathlover6169 2 года назад

It is my pleasure sir

@entity5678 2 года назад

I solved it by cubing a - b = 9 on both sides and then substituting the given values.. a^3 - b^3 - 3ab (a-b) = 729 ( After cubing on both sides) Good problem anyways..

@242math 2 года назад

sure can, -26, thanks for the challenge bro

@PreMath 2 года назад

Glad you think so! You are very welcome. Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@srividhyamoorthy761 2 года назад

Nice

@PreMath 2 года назад

Glad you think so! Thank you! Cheers! 😀 You are awesome Moorthy. Keep it up 👍 Love and prayers from the USA!

@glasssmirror2314 2 года назад

Pls @ 0:38 I got (a-b)(a^2-2ab+b^2) but you got +ab while I got -2ab pls help

@asalamkamal6365 2 года назад

1:35 I don't understand why you added 2ab+3ab Can you explain this to me

@chittella1 2 года назад

In order to bring some portion into (a-b)^2 pattern, ab is replaced by -2ab+3ab whose net is ab only.

@GG12917 2 года назад

@murthys743 2 года назад

could you increase the difficulty

@PreMath 2 года назад

More to come! You are awesome. Keep it up 👍

@murthys743 2 года назад

@@PreMath thanks sir sir , i am preparing for an exam i can share some questions from my sample paper , could you please gather such similar questions of the same difficulty level . RN i can share the portion of the exam , could you ask questions from those topics Progressions, Quadratic equations, Trigonometry, Polynomials Circles it could be really helpful. your videoes are really helpful. Thanks Sir could i share the questions of the sample paper via mail?

@suntipongvisetchaisri9084 2 года назад

-26

@giuseppemalaguti435 2 года назад

-26,lho fatto a mente, magari ho sbagliato... Ah ah... Ho utilizzato la formula della differenza di cubi...

@preetib6819 Год назад

Your first equation is not possible x^n+y^n can never be equal to z^n according to formats last theorem

@murthys743 2 года назад

sir , i am preparing for an exam i can share some questions from my sample paper , could you please gather such similar questions of the same difficulty level . RN i can share the portion of the exam , could you ask questions from those topics Progressions, Quadratic equations, Trigonometry, Polynomials Circles your videoes are really helpful. Thanks Sir could i share the questions of the sample paper via mail?

@sigmamaleslogokijalegi6683 2 года назад

Are u from India?

@murthys743 2 года назад

@@sigmamaleslogokijalegi6683 yeah

@sigmamaleslogokijalegi6683 2 года назад

U must be in 10 grade?

@PreMath 2 года назад

Sure! Dear Murthy, I've already uploaded videos on progressions, quadratic equations, Trig, Polynomials. Please go to PreMath channel and search in the magnifying glass. Please check out this playlist: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-kJ5vJyuSWok.html Keep it up dear and all the best!

@murthys743 2 года назад

@@PreMath thanks a lot

@djtmaga639 2 года назад

A good question is “What are a and b ?”

@PreMath 2 года назад

Glad you think so! I left that task to my smart audience... Thank you! Cheers! 😀 You are awesome MAGA. Keep it up 👍

@Frank_Omar 2 года назад

in this problem we can conclude from b is a negative number and a is positive

@PreMath 2 года назад

Thank you Mark for the feedback! Cheers! 😀 You are awesome. Keep it up 👍

@nickharland9207 2 года назад

Untrue. Both are complex numbers

@Teamstudy4595 2 года назад

Ans : ab = -- 78

@pornhubxuxx 2 года назад

Tahw

@rudychan2003 2 года назад

a & b Are Not Unidentify!! Root of √-23 is not real, is an error!! False Question ! 😕

@carlinoiavarone8342 2 года назад

Sorry but -81 + 27 is -54 !!!

@ssjbevegeta3008 2 года назад

The correct answer is -26

@billyallen7186 2 года назад

27 must be divided by 9 at first

@ssjbevegeta3008 2 года назад

@@billyallen7186 how did you do it ? I simply used (a-b)³

@billyallen7186 2 года назад

@@ssjbevegeta3008 I just tried to answer Carlino's statement based on this video. Yeah i got -26 too.. ab = {(a³ - b³) - (a-b)³} / 3(a-b) ab = (27 - 9³)/3(9) ab = 27/ 27 - 9³/27 ab = 1 - 27 ab = -26