21prophet Sir, how did u get :
3^2 + 2^1 + 1^2 in ur very first statement???
BTW is Cauchy - Shwarz needed 4 JEE??
if 3a + 2b + c =7
find the minimum value of 100 (a2 + b2 + c2) ?
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22 Answers
341Sry, thats supposed to be 32+22+12
The thing is, if you know the inequality, using these constants will follow immediately. For JEE dont bother about this inequality.
21341@manipal: chote bhai, just look up Cauchy Schwarz Inequality in wikipedia
waise, this will not come in jee or aieee etc. so dont bother about it right now
11HEY ANKIT
HE DESERVES RESPECT
HE IS A TEACHER AND NOT AN ASPIRANT
WAISE SIR MUJHE KUCH SAMAJH NAHIN AAYA [2][2][2]
1humlog baki sab ko doob marna chahiye .. chale hai iit clear karne .. aur yeh simple sum nahi bana ... [186]
341you asked for values of a,b and c. So i thought you might like to confirm whether thats right or wrong.
In any case, by Cauchy Schwarz Inequality, we have
(3^2+2^1+1^2)(a^2+b^2+c^2) \ge (3a+2b+c)^2 = 49 \Rightarrow a^2+b^2+c^2 \ge \frac{49}{14}
Hence 100 (a^2+b^2+c^2) \ge \frac{49}{14} \times 100 = 350
Equality occurs when \frac{a}{3} = \frac{b}{2} = \frac{c}{1} using which you get the values given.
1arey yaar .. koi toh kuch socho... aise nahi iit crack kar sakenge ...
1very easy question .. but of iit 4th year level
(this was just a bad joke .. this question is very well there in our syllabus ...) ..
21Ankit : UR a is crrct, but b and c are wrong......
I got a much leser value than wat u got.....
BTW IS MA ANS. CRRCT????
1soln .. don't see before u try ...
minimum value for the eq.. a2 + b2 + c2 is when a = b = c or
3a + 2b + c = 7 .. or 6a = 7 .. a = 7/6
100(3 (7/6)2) = 408.33
there are 100% chance of my soln. being wrong .. because by hit and trial a = 4/3 , b = 1 , c = 1 i got value as 377.77
1a,b,c can take all real values ...
[50]
[50]
72.309 .. tapan how did u get this result ...
11SOMETIMES LOGIC RULES OVER THE STANDARDS METHODS
MY LOGIC a2+b2+c2 is always going to be positive
SO U WONT GET ANY PROFIT BY TAKING A NEGATIVE NUMBER
SO THIS WOULD HAVE MIN WHEN
a=1 b=2 c=0
a=2 b=0 c=1
so i think it should be 500
please confirm it