Inequality/subst qn

zeromeyzl · #1 $Old$ November 5th, 2008, 11:32 PM

By using the subst u = e^(-x/2) or otherwise (pls don't do otherwise!) solve inequality e^-x > 4e^-(x/2) + 4

My ans is x < -2 ln (2+2sqrt2)...not sure if correct!

thisisme · #2 $Old$ November 6th, 2008, 12:37 AM

From the substitution you get: $U^2>4U+4$
rearrange to get $u^2 - 4U - 4>0$
solve to get $u=2+\sqrt{8}$ and $2-\sqrt{8}$
Yes, just following through on paper and it looks correct. Double check that the inequality symbol is the right way round still (i havent so im not saying it is wrong).