Solve the inequlity. x^4 < 36x^2

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the inequality:

x^4 < 36x^2

Move 36x^2 to the left side so the right side is 0.

==> x^4 - 36x^2 < 0

Now we will factor x^2.

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

Now factor between parentheses.

==> x^2 (x-6)(x+6) < 0

==> x^2 is always positive.

==> Then we will solve the inequality for (x-6)(x+6) <0

==> (x-6) < 0 and (x+6) > 0

==> x < 6 and x > -6

==> -6 < x < 6

But we know tha x= 0 is not in the domain.

==> x in (-6, 0)U(0,6)

B

OR

==> (x-6)>0 and (x+6) <0

==> x > 6 and x<-6

==>`x in phi.`

`` Then the answer is the interval (-6,0)U(0,6)

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