Given:
a,b,c >0 and a+b+c=1 ;
P=(1/a)+(2/b)+(3/c);
1)Find the minimum value of P;
2)Does P have maximum value ?
(In reply to
re: A better way to solve this ! by friedlinguini)
If we have a, b
We always have : a^2 + b^2 >= 2ab
because: (a-b)^2 >= 0 (always right)
or : we have a, b >0 we will have: a+b >= 2*sqrt(a*b)
You see it.
We usually use cauchy's inequality to finding minimum value.
In this puzzle, No maximum value because we easily see if we let a=0.000000000000001...... or b=......
We can't find its maximum value.
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Posted by vohonam
on 2002-06-21 13:58:48 |
Cauchy's inequality !
