Question

(n+469)^(1/3) - n^(1/3) > 1,
what's the largest n possible??

Answer 1

\[0\leq n<1728 \]

Answer 2

how u got it?

Answer 3

(n+469)^(1/3) > 1 + n^(1/3)
cube both sides
n+469 > 1 + n + 3(n^1/3) + 3(n^2/3)
=>468/3 > n^1/3 + n^2/3
=>3n^2/3 + 3n^1/3 - 468 <0
its a quad eqn in n^1/3
=>3(n^1/3 -12) (n^1/3 +13)<0
our soln will be
n^1/3 <12
=>max value of n is 1728 <--our ans..

Answer 4

ok,, i understand.. so if n is a integer, then n=1727??

Answer 5

yep,,am sorry..if n is integer,,then 1727 is the ans..

Answer 6

ok, thank' ya for ur explaination..
case closed, hehe..