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?
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:
$\displaystyle (\sqrt{a}^2+\sqrt{b}^2+\sqrt{c}^2)((\frac{1}{\sqrt {a}})^2+(\frac{1}{\sqrt{b}})^2+(\frac{1}{\sqrt{c}} )^2)\ge (1+1+1)^2=9$
cqfd
@+