proving

• July 22nd 2009, 11:01 PM
nh149
proving
how can i do
(a+b+c)(1/a + 1/b + 1/c)>= 9

is there any theorem to use?
i dont know theorems based on this..
can u help me with this? (Lipssealed)
• July 22nd 2009, 11:05 PM
pomp
Quote:

Originally Posted by nh149
how can i do
(a+b+c)(1/a + 1/b + 1/c)>= 9

is there any theorem to use?
i dont know theorems based on this..
can u help me with this? (Lipssealed)

Without conditions on a, b and c this question makes no sense
• July 24th 2009, 10:03 AM
J.R
actually, we must just precise that a, b , c are three positif reals not null.

indeed, we can apply the Cauchy-Schwarz's inegalitie:

we have directly:

$(\sqrt{a}^2+\sqrt{b}^2+\sqrt{c}^2)((\frac{1}{\sqrt {a}})^2+(\frac{1}{\sqrt{b}})^2+(\frac{1}{\sqrt{c}} )^2)\ge (1+1+1)^2=9$

cqfd

@+