Recent content by physion

Apologies, doesn't my line of reasoning rule out all k > 3, not everything except it? Also, my argument should indeed instead specify x 'more than or equal' to 0 and 'non-negative' instead of 'positive', but the line of reasoning should still hold.

Ah, thanks! My reasoning didn't really make much sense looking back on it now. Let's say that, for negative k, we use ##k = -n## where n > 0, so we have ##(x-n)^3 = x^3 + 8x^2 - 6x + 8## Importantly, ##8x^2 - 6x + 8 > 0## for all positive x. However, upon expanding, and canceling x^3 on both...

As shown above, ##x^3 < y^3## (i.e. the case where k = 0) --> ##x < y## , and thus ##k > 0## Similarly, ##y^3 < (x+3)^3## --> ##y < x + 3## We are left with ##k = 1, k = 2.##

Hi everyone! I'm in 9th grade and I've been teaching myself (albeit haphazardly) physics and maths for a while now in order to escape the boredom of the classroom, but I thought it might be a good idea to seek some input now and then. :) I look forward to making some mistakes--just hopefully...