Math Olympiad | A Nice Algebra Problem | VIJAY Maths
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- เผยแพร่เมื่อ 22 ส.ค. 2024
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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.
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
Very Good 😊
this is the normal method.
Why VIJAY does use the complex method?
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)
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
Bilkul
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
About quadrilateral th-cam.com/video/fZQF61aZoGM/w-d-xo.html
Nice example with enough best tricks 🎉
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
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...
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
Yes answer is same but don't leave denominator as rational , do rationalise the denominator 👍
Find out the ratio of a:b:c by dividing those eqs, then just use k method
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.
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
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
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
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
(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)
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.
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
Thanks for sharing!
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
Well try 👍
SENSATIONAL PROFESSOR!
Thanks
a100, b-0c-200
100+0+200=300
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
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Do we other method? Comment below 🙏🏻🙏🏻🙏🏻
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.
@@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 👌🏼👌🏼👌🏼
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.
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
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
Great explanation
Glad you liked it
It's completed .If we do by ratio of proportion, answer will be 11 and very easy
(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)
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...
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
Good, very good 👍
Muy bueno. 👍👍👍
Thank you!
👏👏
55√6/3
Super explanation 👍
Thank you ⚘️
How to got A2 value .u r not displayed. Display that value also
Why this lengthy method
The problem can be solved by various methods Instead of solving in shortcuts we should also know the other ways too.
But olympiad questions should be solved in less than a minute. I m too tutoring for olympiad
Bhai tum solution de do.....jo padha Raha usko bhi anguli karte hai....tum ek TH-cam channel bana lo @@crkr1955
Why u have put bc in the nr. ..plz.give mathematical reason
Took 11 min for one min problem !
20000
Jai shree Ram 🙏
Jai shree Ram🙏🙏
This math is related to which standard/class?
Проще почленно перемножить ивозветсти в квадрат сумму аивис
जि हां
Why discarded negtive root ?
Why need payment for download
Keine gute Lösungsmöglichkeit ... statt in einander zu multiplizieren , wäre besser dividieren ...
You for got to carry the ±.
a+b+c =600 😅😅😅😅😅
Thora bare karkay likhia
Thik hai 👍
Easy,/
Ask an expert .extra 2AB qualified hole sq man
A=100
B=0
C=200
Why do you call it math olympiad?
your explanation is for 3rd graders.
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.
hopeless solution. This man made it complicated.
Thank you so much ⚘️
It shows your mindset how you are having😊
खालि नाम कृष्ण रखलेने से कुछ नहि होता बल्कि स्वभाव भी कृष्ण कि तरह अछि रखना चाहिए