## LifeIsADangerousGame one year ago Can anyone give me an explanation for this? http://cdn2.hubspot.net/hub/360031/hubfs/body_arithmetic-1.jpg?t=1439394385622&width=504

1. ganeshie8

$$n^2\ge 1\tag{1}$$ $$\implies |n| \ge 1$$ $$\implies n^2\ge n\tag{2}$$ adding both equations yields $$n^2+n^2\ge 1+n$$ $$\implies 2n^2-n\ge 1$$

Would testing each answer out work as well? I tried, but it didn't work out for me. Memorizing isn't my strong point, so I'm trying to figure out other methods.

3. Nnesha

i would do that.^^^^ :P

4. Nnesha

i'll pick a number for n let n=-6 $2(-6)^3+(-6)=2(-216)-6=-438$ so $\ \cancel{E}$ $(-6)^3 +(-6) = -216-6 =-222$ D isn't correct $\ \cancel{D}$ $(-6)^2+(-6)^3 = 36-216=-180$ $\ \cancel{C}$ now there are 2 possible options hmmm$\rm 2(-6)^2-(-6) ~and~(-6)^2-6$

they both end up positive?

6. Nnesha

yeah...

so how do I know which one is correct?

8. Nnesha

$\rm 2(-6)^2-(-6) ~and~(-6)^2-6$ $2(36)\color{reD}{+}6 ~~~~~~~~~~~~~~~~~~~ 36\color{reD}{-}6$ hmmm i guess ^^addition ^subtraction different signs hmm LOL sometimes i use my own method *sigh*

9. Nnesha

anyway i'll work on this later i'm sleepy rn....

oh okay, thanks for your help!

11. Nnesha

np :)