Question

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

Answer 1

\(n^2\ge 1\tag{1}\)
\(\implies |n| \ge 1\)
\( \implies n^2\ge n\tag{2}\)


adding both equations yields
\(n^2+n^2\ge 1+n\)
\(\implies 2n^2-n\ge 1\)

Answer 2

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.

Answer 3

i would do that.^^^^ :P

Answer 4

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\[\rm 2(-6)^2-(-6) ~and~(-6)^2-6\]

Answer 5

they both end up positive?

Answer 6

yeah...

Answer 7

so how do I know which one is correct?

Answer 8

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

Answer 9

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

Answer 10

oh okay, thanks for your help!

Answer 11

np :)