Question

x^4 < 36x^2 (divide both sides by x^2)
x^2 < 36 (take the square root of 36)
x < 36 (or does the sign change to > here?)
My brain feels fried doing all my of precalc questions!x^4 < 36x^2 (divide both sides by x^2)
x^2 < 36 (take the square root of 36)
x < 36 (or does the sign change to > here?)
My brain feels fried doing all my of precalc questions!@Mathematics

Answer 1

the sign of the equality does not change, there fore it would not switch. also it would be x<6, not x<36

Answer 2

whoops! See, my brain is fried! lol

Answer 3

-6<x<6

Answer 4

oh... forgot the \[\pm\] lol

Answer 5

yeah i was going to say treat x^2 as like |x|

Answer 6

sqrt(x^2)=|X|

Answer 7

So the set notation would be {x|-6<x<6}, right?

Answer 8

i would have no clue, i don't use set notation XD

Answer 9

umm. not really

Answer 10

Outkast, :P

Answer 11

x^4-36x^2<0
x^2(x^2-36)<0
but since x^2>0
then x^2-36<0
then -6<x<6

Answer 12

ghass, where are you getting the whole x^2(x^2 - 36) from?

Answer 13

yeah well right now i'm in linear algebra talking about spaces and there is so many notations and ways of writing that i just write the answers out full like

W exists in V
instead of
\[W \in V\]

Answer 14

just factorizing...never cancel any term..

Answer 15

This pre-calculus class is the end of me.

Answer 16

ghass is correct you are getting rid of useful information

Answer 17

you'd have to check 2 cases

Answer 18

yes, the answer in set notation is

\[\Large \{x|-6<x<6\}\]

Answer 19

I'm still lost so to how it got that way. Such a simple problem has me dumbfounded.

Answer 20

x^4 < 36x^2


x^4 - 36x^2 < 0


x^2(x^2 - 36) < 0


Since x^2 > 0 for all x, this means that you can divide both sides by x^2 and the sign will not flip


(x^2(x^2 - 36))/(x^2) < 0/(x^2)


x^2 - 36 < 0


(x-6)(x+6) < 0


Now use a graphing calculator, or plug in test values, to see that the solutions are


x > -6 and x < 6


which combine to


-6 < x < 6

Answer 21

an extra hint:the sign of a quadratic equation ax^2+bx+c is opposite to a between the roots and the same as a outside them...

Answer 22

Thanks, Jim! Thanks, Ghass!

I appreciate your help in showing me.