Hi. I'm doing a project on the fib. sequence, but since some of my math skills are weak, and I do not know the exact project I want to (just that I want to do something related to the seq), my teacher reccommended that I do some math problems over the break, so I can get some higher level math practice and more creative.
However, on a list of 15 practice qs, I haven't been able to do more than 2 in the two weeks I've been working on it (a lot, too...)
The two I am most having trouble with follow along with what I have so far.
1. PROVE (ahh) that (x+1)(x^2+1)(x^3+1) is less than or equal to 4(x^6+1) for all real numbers x.
So far, I've only been able to, basically, simplify it. I got to the following (and after that, I just seem to be going in circles): x^4+x^3+2x^2+x <= 3x^6. I know it isn't much. It took a page of math, and it is the seventh one I got, so I'm not sure if that is right. I keep finding mistakes in my work, but so far, that one seems right. That's all I have for this...also, just my rationale that the left side isn't "growing" as quickly, but I know that is not a "proof," so..yeah.
2. What is the largest number of points that can be placed in (or on the boundary of) a 2x2 square so that the distance between each pair of pts is at least one? Justify your answer.
I got the answer 9 - with a pt at each vertex. I tried to find other ways and couldn't. I can't justify it really...I just did it experimentally, so I'm not sure it is right either.
Thanks for helping. I am completely exhausted. I seem to have been going in circles and just doing nothing while trying so hard for days now.