We have :
x^2+xy+y^2=3 and
y^2+yz+z^2=16
A=xy+yz+zx
Find the maximum value of
A.
Find x, y and z when A=max value.
(Remember the category)
(In reply to
Methods to solve this by vohonam)
We use 2 inequalities :
1)Cauchy's inequality :
a + b >= 2*square root of (a*b) ; (a,b>0)
or a common Chauchy's inequality :
((a1+a2+a3+.....+a(n))/n)^n >= a1*a2*...*a(n)
"=" when a1=a2=...=a(n)
2)Chebyshev's inequality :
absolute value of (a*x+b*y) <= square root of ((a^2+b^2)*(x^2+y^2))
"=" when a/x=b/y
Those inequalities are easy to prove.
From these, I hope that you can solve this problem
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Posted by vohonam
on 2002-06-19 17:28:58 |
re: Methods to solve this
