Japanese | Can you solve this ? | A Nice Math Olympiad Algebra Problem.
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- เผยแพร่เมื่อ 5 ก.ย. 2024
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Multiply ab bc ca . We get a square, b square c square. So we get abc whole square. By way of this we get the value of abc. Then divide by the values of ab, bc, ca and get the value of a,b,c. Then just add and get the value of a + b + c. Simple
Simple in three steps🎉
This method is easier than your solution procedure sir.
a= √150 ; b=√(200/3); c=√600
a+b+c= 5√6 + 10√2/√3 + 10√6
=5/√6+10√6/3+10√6
= √6(5+10/3+10)
=√6(15+10/3)
=√6(55/3)
a+b+c = 55√6/3
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
th-cam.com/video/TDFfjc00nvk/w-d-xo.html
Your method seems much simpler but I still had problems following it. Where can I go to practice your method?
@@joseeoliviero6078 How do you think about this method?
(3) / (1) gives c / b = 3 : 1
(2) / (1) gives c / a = 2 : 1
∴ a : b : c = 3k : 2k : 6k
By (1), 6k^2 = 100
∴ k^2 = 50/3
k = +- (5√2) / √3
Their sum equals 11k.
∴ a + b + c = +- (55√2) / √3
= +- 55√6 / 3
Done.
@@N_Kumar26 And you missed the negative solution
This type of question is asking in exam then you quickly make answer. You can practice your self like ab=400
bc=200
ca=800 find value of a^2+b^2+c^2
Here you tube link you could know more class wise questions and answers.
th-cam.com/video/TDFfjc00nvk/w-d-xo.html
100+200+300=600
a+a+b+b+c+c=600
a+b+c. =300..very simple .and easy..Total letter =600..than.you take half..
Of Total letter equal 300..
It is too lengthy procedure
Lengthy process,find a²b²c² first,then a,b,c ,add three
Сравнив 1-ое и 2-ое видим, что с= 2а.
Из 3-его следует- 2а^=300; отсюда-а=5√6;с=10√6;в=20/√6; в итоге: а+в+с =55√6/3;Самое простое решение.
А сравнить зачем?
Вроде выражаем, подставляем - должно решаться элементарно (система для пятого класса школы).
After you got a^2 b^2 and c^2 you could radicalize both side and add the results. Before of you go a lot of steps but the video is good keep it up🎉
a+b+c also admits its negative value. With a b c negative.
a=100,b=0 c=200
No need of formula
Yes directly we can do.
Excellent sollution
1- ab = 100
2. bc = 200
3. ca = 300
1*2*3
ab*bc*ca = 100*200*300
(abc)^2 = 6000000
abc = (√ 6000000 ) = √ (6 * 1000000 ) = √6 * 1000 = 1000 √6
=>1 ab = 100 ,.abc = 1000 √6 , 100 * c = 1000 √6 , c = (1000 √6 ) / 100 = 10√6
=>2 bc = 200 , abc = 1000 √6 , 200 * a = 1000 √6 , a = (1000 √6) / 200 = 5√6
=>3 ca = 300 , abc = 1000 √6 , 300 * b = 1000 √6 , b = (1000 √6 ) / 300 = (1000/300) * √6 = (10/3) * √6
a+b+c = 10√6 + 5√6 + ((10/3) * √6) = (10+5+(10/3) √6 = (15+ 10/3 ) √6 = (45/3 + 10/3 ) √6 = (55/3 ) √6
My God!
How to have such intuition!
brother...abc is ±√6000000
@@seekingCK OK. a+b+c = ±(55/3)√6
c / b = 3 : 1
c / a = 2 : 1
∴ a : b : c = 3k : 2k : 6k
By (1), 6k^2 = 100
∴ k^2 = 50/3
k = +- (5√2) / √3
Their sum equals 11k.
∴ a + b + c = +- (55√2) / √3
= +- 55√6 / 3
Done.
Easiest solution
Hats off
simplest one.
Very nice. I just recollected my mind for 70 years back momery
To simplify, let p=10a, q=10b and c=10c then
pq=1,qr=2, rp=3 and pqr^2=6
pqr=√6 or pqr=-√6
For pqr=√6
From pq=1 and pqr=√6, r = √6 since pq = 1
Also q = √6 / 2, p = √6 / 3
Finally a+b+c
= 10p+10q+10r
= 10 (p+q+r)
= 10 (√6/3+√6/2+√6)
= 10 (11√6 / 6
= 110√6 / 3
= 55√6 / 3
For pqr = -√6, a+b+c = -55√6/3
Sol: 55√6 / 3, -55√6 / 3
-(55√6)/3 or (55√6)/3
Yeah he missed the negative solution
i think so.
why negative
@@is7728why negative
(a+b+c)^2=6050/3
→a+b+c=+-√(6050/3)
___ ___
and in the case that all of a,b,c is negative ...
could you make
a+b+c=negative
How do you think about this ?
Thanks sir 🎉
Your welcome. Thanks
ab*bc*ca=(abc)^2=100*200*300. Then abc=1000*6^0.5. Then a=abc/bc=5*6^0.5
b=abc/ca=10/3*6^0.5
c=abc/ab=10*6^0.5
Then a+b+c=6^0.5(5+10/3+10)=55/3*6^0.5
abc=100c
abc=200a => 11abc=600(a+b+c)
abc=300b
(abc)^2 = 100*200*300 => abc = +- √(100*200*300) = +- 1000*√6
a+b+c = 11abc/600 = +-11*1000*√6/600 = +-110/√6
Good idea
Hello why are you going this much critical. Easy & simple way A+B =100, (A is 100& B is 0). B&C=200(B is 0&C is 200), then. C+A=300(C is 200& A is 100).A+B+C= 300. 👌
Simple and super..
Спасибо. Я бы решила иначе, но ваш метод тоже интересен
Once you have values for a, b and c, you can simply add them.
Чувак не правильно решил: сократив корень и квадрат скобок, должен был получиться модуль, и на выходе два решения
2a+2b+2c=600
Dived by 2
a+b+c =300
Right short answer
There is another short solution if we divide equation1 buy eq2
சிறப்பு
Your welcome
Beautiful
Thank you! Cheers!
a
ab+bc+ca=600. 2(a+b+c)=600. a+b+c=300
How 2a+2b+2c= ab+bc+ca ??????
how ab+bc+ca will become2(a+b+c) ????? New mathematical Theory...
ab.bc/ac=b^2=200/3
b=20/root 6
similarly
a=30/root 6
c=60/root 6
a+b+c=110/root6
this is shortest method
awesome
Your welcome
Total a+ b + c =600
a + b + c = 300
(a : 100 ; b: 0 dan c : 200 )
is approximately 44.9073
a=100, b=0, c=200
A100. B0. C200
how is c/b 3:1? how do you kno this? can you explain please
you nedd not write every line ( a+B+C)*2put lhs an d rhs to denote left and right
c=10sqrt6
b=10sqrt6/3
a=5sqrt6
ab±bc±ca=600
2(a±b±c)= 600
a±b±చెప్పు =300
a=12.5,b=8,c=25
👏👏
Your welcome
ab.bc.ca = a²b²c² = (abc)² = 100 . 200 . 300 = 6 . 10⁶
then abc = 6.10⁴, a.bc = 6.10⁴ , a.200= 6.10⁴ so a=3.10² , etc
a+b+c=250
a+b+c=45.5
Mistake ho chuki hae pl rechek caculation.
There is a easiest way to solve this problem than that.
What is final result?
Прикольно, но всегда мучает вопрос - нафига это?
Ab+bc+ca =100+200+300
2(a+b+c) = 600
A+b+c= 600/2
A+b+c = 300
6oo/11 ans
Есть ещё одно решение с минусом
350
🤔
You have left abc😮
B= 0
It's ok but what is useful in our regular life.
350
C=200
A=100
B=0
Simple
105
302
,२००प्रतेकी
It's ok? You lose the same with minus
Three hundred
600
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10
401
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100
300
B=0
डोक्यावरुन गेले.
you are saying that a+b+c is equal to the numerator
500
D 200 E 900 F2
800
11
Okay but what is the numerical value ??? That’s what my question is
The numerical value could have been found about 1/3 of tge way in. YES, it would have been approximated, the precision would depend upon how many decimal places you choose to use.
@@robertloveless4938
No more than 2-3 decimal places would be fine for me.
Цікаво 😊❤
Your welcome!
Too lengthy
A- 100
B- 0
C- 200
A+B=100 100+0=100
B+C=200 0+200=200
C+A=300 200+100=300
A+B+C=? 100+0+200=300
A. 300
సి స్క్వేర్ 600 లు యేమైంది
Very primitive methods
এত দীর্ঘ করে ভাল শিক্ষক অংক করে না। কথা শুদ্ধ করে পাঠদানে আশা উচিত।
またまた、虚数根つかうの😂辞めなよ
Modi ko bolo, woh bahut expert hai.
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