Question

number fun ( ͡° ͜ʖ ͡°)

Answer 1

l,m,n are positive real numbers such that \[l^3+m^3=n^3\]prove that \[l^2+m^2-n^2>6(n-l)(n-m)\]

Answer 2

i^2+m^2-(i^2+m^2)>6((i+m)-l)((i+m)-m)
0>6(m+i)

Answer 3

if \(l>n\) or \(m>n\) then the left side of the inequality is a positive number and the right side is a negative number.

if \(l>n\) and \(m>n\) then the right hand side will be positive, so I have no proof, oh well, sorry.

if \(l<n\) and \(m<n\) then I also have no proof so I guess I just wasted my time, but hey I proved it for like infinitely number of cases as long as this is true, the inequality will be true:

\[l<n<m\] Haha oh well. I just wanna avoid playing with binomial expansions xD

Answer 4

stalker

Answer 5

>.>

Answer 6

:)