SOLUTION: Someone please could help me with that? Solve the nonlinear inequality. Express the solution using interval notation. x^2(x^2 − 36) ≥ 0

Algebra ->  Inequalities -> SOLUTION: Someone please could help me with that? Solve the nonlinear inequality. Express the solution using interval notation. x^2(x^2 − 36) ≥ 0      Log On


   



Question 947633: Someone please could help me with that?
Solve the nonlinear inequality. Express the solution using interval notation.
x^2(x^2 − 36) ≥ 0

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Express the solution using interval notation.
x^2(x^2 − 36) ≥ 0
--------
Factor::
x^2(x-6)(x+6) >= 0
----------------------
Draw a number line and plot x = -6, x = 0, x = 6
-------------------------
Some Solutions:: x = 0, x = -6, x = 6
-------------------------
Check a value in each of the intervals to find solutions for the inequality::
x^(x-6)(x+6 > =
Check x = -10:: +*-*- > 0 :: true
----
Check x = -3:: +*-*+ > 0 :: false
----
Check x = 3:: +*-*+ > 0 :: false
----
check x = 10:: +*+*+ > 0 ;; true
----
Solutions:: (-oo,-6] ; (0) ; [6,+oo)
==============
Cheers,
Stan H.
--------------

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%28x%5E2+-36%29+%3E=+0

x%5E4+-36x%5E2+%3E=+0
x%5E4++%3E=+36x%5E2.....simplify
x%5E4%2Fx%5E2++%3E=+36x%5E2%2Fx%5E2
x%5E2++%3E=36=>x+%3E=sqrt%2836%29 =>x+%3E=6=>x+%3C=-6

solution interval:
if x+%3E=6: [6,infinity)
ifx%3C=-6:(infinity,-6]