
solution for inequality
Hi everyone,
I seem to be stuck at solving the following:
$\displaystyle (l1)i+\frac{(ll^2)\sigma^2}{2}\overset{!}>0$
Well, my solution ist: $\displaystyle i\overset{!}<{\frac{l\sigma^2}{2}$
BUT, when I plug in $\displaystyle l=2, l=1, l=2$ with $\displaystyle \sigma^2=0.04$ I only get a correct solution for $\displaystyle l=2$
That is:
$\displaystyle (21)i+\frac{(22^2)0.04}{2}=i0.04\overset{!}{>}0$
and therefore: $\displaystyle i\overset{!}{<}0.04$ which corresponds to $\displaystyle i\overset{!}<{\frac{l\sigma^2}{2}$
However, for $\displaystyle l=2$ I should get: $\displaystyle i\overset{!}<{\frac{(2)\sigma^2}{2}=\sigma^2=0.04$
And here is what I do get for plugging in $\displaystyle l=2$ in the first equation:
$\displaystyle (21)i+\frac{(2(2)^2)\sigma^2}{2}\overset{!}>0$
$\displaystyle 3i\frac{6\sigma^2}{2}=3i3\sigma^2\overset{!}{>}0$
Then my solution is $\displaystyle i\overset{!}{>}0.04$
which is not the same as $\displaystyle i\overset{!}{<}0.04$
What's going on here?
Thank you for your help.