SOLUTION: Solve the following inequality showing your work: |X|=6-X^2

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Question 896466: Solve the following inequality showing your work: |X|=6-X^2
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
  abs%28X%29=6-X%5E2

We square both sides:

  X%5E2=%286-X%5E2%29%5E2

  X%5E2=36-12X%5E2%2BX%5E4
  
  0=X%5E4-13X%5E2%2B36

  0=%28X%5E2-9%29%28X%5E2-4%29

  0=%28X-3%29%28X%2B3%29%28x-2%29%28X%2B2%29

We get 3, -3, 2, -2

But we must check for extraneous answers:

  abs%28X%29=6-X%5E2 
  abs%283%29=6-3%5E2
  3=6-9
  3=-3

3 is not a solution


  abs%28X%29=6-X%5E2 
  abs%28-3%29=6-%28-3%29%5E2
  3=6-9
  3=-3

-3 is not a solution


  abs%28X%29=6-X%5E2 
  abs%282%29=6-2%5E2
  2=6-4
  2=2

2 is a solution


  abs%28X%29=6-%28-2%29%5E2 
  abs%28-2%29=6-%28-2%29%5E2
  2=6-4
  2=2

-2 is a solution

So there are only two solutions, 2 and -2.

Edwin