Math Olympiad | A Nice Algebra Problem | VIJAY Maths

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#exponentialproblems #matholympiad #maths #algebra

[@biswanathbera1260]

Unnecessarily lengthy. Just get abc=√(100×200×300) =1000√6.. a=1000√6/200=5√6, b=1000√6/300=10√6/3 and c=1000√6/100=10√6. Adding a, b and c we get 55√6/3.

[@sy8146]

Thank you for explaining. [My method:] (ab)(bc)(ca)=6,000,000 ∴ (abc)^2=6,000,000 ∴ abc = ±1000√6 ∴ a = (abc)/(bc) = (±1000√6)/200 = ±5√6 b = (abc)/(ca) = (±1000√6)/300 = ±(10/3)√6 c = (abc)/(ab) = (±1000√6)/100 = ±10√6 ∴ a+b+c = ± (5 + 10/3 + 10) √6 = ±(55/3)√6 0, c

[@vijaymaths5483]

Very Good 😊

[@user-ji5su2uq9m]

this is the normal method. Why VIJAY does use the complex method?

[@RealQinnMalloryu4]

10^10 2^52^5 1^12^1 2^1 (b ➖ 2a+1) 10^20 2^55^4 2^1^14 2^1^12^2 1^1^1^1^2 1^2 (c ➖ 2b+1) 10^30 2^55^6 2^1^13^2 1^1^13^2 3^2 (c ➖ 3a+2)

[@dyrattanak2248]

Why you go to far, if we know a,b,c a = √150, b= √200/3, c= √600 a+b+c = √150+ √200/3+ √600= 55/3 √6

[@satyanarayansharma9364]

Bilkul

[@N_Kumar26]

LCM of (1,2,3)=6 6abc=6cx100=600c 3abc=3a×200=600a 2abc=2bx300=600b Add 11abc=600(a+b+c) ab×bc×ca=100x200x300 (abc)^2=(1000)^2×6 abc=1000√6 11x1000√6=600(a+b+c) a+b+c=110/√6=(55√2)/√3

[@N_Kumar26]

About quadrilateral kzbin.info/www/bejne/nIu0d2lnlr-ifa8

[@urmilas5356]

Nice example with enough best tricks 🎉

[@abdeltifelbihel3076]

From 1 and 2 : c=2a From 1 and 3 : c= 3b ca= 300 so : 2a^2= 300 then : a^2= 150 so: a=5√6 * c=2a so : c = 10√6 * b= c÷3 then : b= 10√6/3 a+b+c = 15√6+10√6/3 a+b+c= (45√6+10√6)/3= 55√6/3

[@UrievJackal]

You have just forgotten a minus, while solving a^2=150. Btw, I used the same way. (3)÷(2) gives a/b =3/2 and so forth...

[@Wynb824]

Find out the ratio of a:b:c by dividing those eqs, then just use k method

[@thomasharding1838]

A long time ago you determined that a squared = 150, and b squared = 200/3, and c squared = 600. Extract the square roots of those values and add them up.

[@andreysidor9912]

аb/ac=b/c=100/300=1/3 b=c/3, bc=c^2/3=200, c=√600 b=200/√600, a=300/√600 a+b+c=55√6/3

[@sudhakaranpillai9623]

a=5√6,b=10√2/√3,c=10√6 a+b+c=5√6+10√2/√3+10√6 =15√6+10√√2/√3 =(15√6.√3+10√2)/√3 =(15.3√2+10√2)/√3 =(45√2+10√2)/√3 =55√2/√3=(55√6)/3

[@marcgriselhubert3915]

(a, b and c are of same sign. ab).(bc).(ca) = 6000000 =(abc)^2, so abc = 1000.sqrt(6) or abc = -1000.sqrt(6) *If abc = 1000.sqrt(6) then a = abc/bc = 5.sqrt(6), in the same way b = (10:3).sqrt(6) and c = 10.sqrt(6) Then a +b +c = (55/3).sqrt(6) *If abc = -1000.sqrt(6) then a, b, c are the opposite of the former values and a +b + c = (-55/3).sqrt(6)

[@sie_khoentjoeng4886]

Let p=10a, q=10b, r=10c, then pq=1, qr=2 and rp=3 And (pqr)^2 =6 pqr=√6 or r=√6 since pqr=1 By same way, p=(√6) /2 and q=(√6) /3 Here a+b+c=10p+10q+10r =10(p+q+r) =10(√6+(√6)/2+(√6) /3) = 10 (11/6 √6) = 110/6 √6.

[@tapaspatra6148]

It's completed .If we do by ratio of proportion, answer will be 11 and very easy

[@kennethkan3252]

ab=100 bc=200 ac=300 a:b:c=3:2:6 a+b+c=??? ac=300 a:c=3:6=1:2 a(2a)=300 2a^2=300 a^2=300 a=10✓3

[@satrajitghosh8162]

a b * b c * c a = 6 * 10^6 a b c = 1000 √6, - 1000 √6 a + b + c = 10 √ 6 *(1 + 1/2 + 1/3) , - 10 √ 6 *(1 + 1/2 + 1/3) , a + b + c = 110 /√6, -110 /√6

[@vijaymaths5483]

Yes answer is same but don't leave denominator as rational , do rationalise the denominator 👍

[@kennethkan3252]

ab=100 bc=200 ca=300 (ab)x(bc)x(ca) =(a^2)(b^2)(c^2) =(abc)^2 =100×200×300 =6000000 abc=✓6000000 ab=100 c=✓6000000÷100

[@Rocio62154]

SENSATIONAL PROFESSOR!

[@vijaymaths5483]

Thanks

[@nalapurraghavendrarao6324]

Such a laborious tedious of solving .if you multiply all equations and taking square root We get abc=1000√6 which is equation (4).divide eq 4 by ab,bc ,ca to get a,b,c. Add a,b,c to get required answer.

[@santokhsidhuatla7045]

b=100/a bc=200 C=200/b=200/100. X a=2a Ca=300 2a*a=300 a^2=150 a=150^1/2=12.25 b=100/12.25=8.16 C=300/12.25=24.49 a+b+c=44.90

[@vijaymaths5483]

Well try 👍

[@julietavakian5380]

Your method is too complicated ! I found the result using proportions! b=100/a; b=200/c; 100/a=200/c; a=c/2. Because ca=300, then cxc/2=300; c^2=600;c=10sq.root of 6;a=5sq.root of6; b=10sq.root of6/3; a+b+c= 55sq.root of6/3

[@vijaymaths5483]

Thanks for sharing!

[@somnathkundu7354]

One novel idea. Take Log Base 100 for all the equations and then use Crammers rule. Ohhh. This can't be an olympiad question. This is rudimentary

[@superiorlyrics8326]

👏👏

[@EllmarRosales]

(abc)*2=™[(100)(200)(300)]; abc=(10)[10sqrt(2)][10sqrt(3)]; Then c=10sqrt(6) a=5sqrt(6); b=10sqrt(6)/3 so that a+b+c=[5sqrt(6)]+[10sqrt(6)/3]+[10sqrt(6)] a+b+c=[5+10/3+10]sqrt(6) Or a+b+c=(55/3)sqrt(6)

[@NhaNguyen-cx1ri]

ab=100 bc=200 ca=300 >>a=100/b c=200/b ac=100b×200b 100b×200b =10000b 10000b=300 b=3/100 ab=100>> a=100:3/100 =10000/3 Ca=300 >>c=900/10000 C=9/100 a=10000/3 b=3/100

[@crazyindianvines1472]

Great explanation

[@vijaymaths5483]

Glad you liked it

[@andryvokubadra2644]

ab = 100 bc = 200 ca = 300 =========== Metode I ab*bc*ca = 100*200*300 = 100*6*10000 (abc)² = 100*6*10000 abc = ±10*√6*100 = ±1000√6 a = ab*ca/abc = 100*300/(±1000√6) a = ±30/√6 b = ab*bc/abc = 100*200/(±1000√6) b = ±20/√6 c = bc*ca/abc = 200*300/(±1000√6) c = ±60/√6 a + b + c = ±(30+20+60)/√6 a + b + c = ±110/√6 ========== Methode 2 ab/bc = a/c = 100/200 = 1/2 a/c = 1/2 --> c = 2a bc/ca = b/a = 200/300 = 2/3 b/a = 2/3 --> b = 2a/3 ca = 300 (2a)a = 300 2a² = 300 a² = 150 a = ±5√6 a + b + c = a + 2a/3 + 2a a + b + c = 11a/3 a + b + c = 11(±5√6)/3 a + b + c = ±(55√6)/3 a + b + c = ±110/√6 ========= Method 3 As video ========= • • • Do we other method? Comment below 🙏🏻🙏🏻🙏🏻

[@vijaymaths5483]

Good try..Thanks for sharing! 😃 Yes there is also one more method as well to solve but it will take longer video length so I couldn't solve that but if you wish I can make a separate video by using another method.

[@andryvokubadra2644]

​@@vijaymaths5483 3:26 with this result, it's 4th methode 😊😊😊 You can check manually the comment below. . . then you resume it for some methodes in other video 👌🏼👌🏼👌🏼

[@crkr1955]

Very lengthy procedure indeed Simply find out c/a You have ca Multiply U get c Then finf out a n b Add a+b+c This is done in 40vsec Any sum should b done in 1 minute only

[@vijaymaths5483]

Good, very good 👍

[@mythilir1358]

a100, b-0c-200 100+0+200=300

[@ShivayVerma-h2y]

Aaj kal compitition ka jamana latest technology ka tabhi job milti hai smart work and get the job

[@kidas0808]

I have another solution for this math problem. a*b=100: b*c=200: c*a=300: b=100/a: b=200/c: c=300/a 100/a=200/c: a=sqrt(150): b=100/sqrt(150): c=300/sqrt(150) a+b+c=sqrt(150)+100/sqrt(150)+300/sqrt(150)=550/sqrt(150)=302500/150=2016.666666...

[@Fmacian59]

Muy bueno. 👍👍👍

[@vijaymaths5483]

Thank you!

[@Srikanthvedios]

How to got A2 value .u r not displayed. Display that value also

[@sumit-mn6ys]

Super explanation 👍

[@vijaymaths5483]

Thank you ⚘️

[@crkr1955]

Why this lengthy method

[@vijaymaths5483]

The problem can be solved by various methods Instead of solving in shortcuts we should also know the other ways too.

[@crkr1955]

But olympiad questions should be solved in less than a minute. I m too tutoring for olympiad

[@brajeshreshamiya3821]

Bhai tum solution de do.....jo padha Raha usko bhi anguli karte hai....tum ek KZbin channel bana lo ​@@crkr1955

[@prakritipattanayak7423]

This math is related to which standard/class?

[@kadappadevarmani9616]

Why u have put bc in the nr. ..plz.give mathematical reason

[@AllanPoeLover]

Why discarded negtive root ?

[@Danieswors]

55√6/3

[@nantesloire]

Keine gute Lösungsmöglichkeit ... statt in einander zu multiplizieren , wäre besser dividieren ...

[@subbaraob8474]

Why need payment for download

[@ajeethpandey]

Took 11 min for one min problem !

[@RayArias]

You for got to carry the ±.

[@chesettianandkumar4492]

Jai shree Ram 🙏

[@vijaymaths5483]

Jai shree Ram🙏🙏

[@user-rw7de5oh1b]

Проще почленно перемножить ивозветсти в квадрат сумму аивис

[@vijaymaths5483]

जि हां

[@satyapatrudu9802]

20000

[@jamesjacob8863]

a+b+c =600 😅😅😅😅😅

[@sanjeevroy824]

Thora bare karkay likhia

[@vijaymaths5483]

Thik hai 👍

[@raghuvennelakanti2851]

Why do you call it math olympiad? your explanation is for 3rd graders.

[@vijaymaths5483]

Math Olympiad organises exams from students of grade 1 to grade 12 here I can't mention a particular grade for every problem so it's kind of knowledge to share with everyone for quick practice.

[@ShivayVerma-h2y]

Itna time na lagta solve karna mai

[@vijaymaths5483]

Thank you for solving in 10 seconds , you're a great mathematician🙌🙌

[@trevordsilva506]

Ask an expert .extra 2AB qualified hole sq man

[@KhinMaungSan-qc9uv]

Easy,/

[@guerrino50]

A=100 B=0 C=200

[@krishansaxena7889]

hopeless solution. This man made it complicated.

[@vijaymaths5483]

Thank you so much ⚘️ It shows your mindset how you are having😊

[@prabhushettysangame6601]

खालि नाम कृष्ण रखलेने से कुछ नहि होता बल्कि स्वभाव भी कृष्ण कि तरह अछि रखना चाहिए