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sinusoidal

  • 2 years ago

2|x-1| < x^2 answers are: x < -1 - sqrt(3) or x > -1+sqrt(3) I'm having trouble coming up with these solutions. Could someone help me with the steps?

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  1. myininaya
    • 2 years ago
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    Did you try looking at 2|x-1|=x^2 first When we have |f(x)|=a, we try to solve this by doing f(x)=-a of f(x)=a Now keep in mind that a needs to be positive or 0. Guess what? x^2 is a positive number or 0.

  2. myininaya
    • 2 years ago
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    I'm tell you to solve the following 2(x-1)=x^2 or 2(x-1)=-x^2

  3. sinusoidal
    • 2 years ago
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    I've got it now. I thought that I tried that before, but I think I was just making so many mistakes that I became too sloppy and frustrated

  4. sinusoidal
    • 2 years ago
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    thanks

  5. sinusoidal
    • 2 years ago
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    getting rid of the inequalities made it a lot simpler.

  6. sinusoidal
    • 2 years ago
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    how would you know how to replace the inequalities back into the answer?

  7. sinusoidal
    • 2 years ago
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    analytically, I mean

  8. myininaya
    • 2 years ago
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    One of the equations you solve, you will get a complex answer. The other equation you solve, will give you two real solutions. You should see x=-1+sqrt(3) or x=-1-sqrt(3). You can test intervals to see where we have 2|x-1|<x^2 |dw:1380904061968:dw|

  9. myininaya
    • 2 years ago
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    |dw:1380904086865:dw| 2|-10-1|<10^2 True/False 2|0-1|<0^2 True/False 2|10-1|<10^2 True/False

  10. myininaya
    • 2 years ago
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    The inequalities that come back true are the intervals you want to include in your solution.

  11. myininaya
    • 2 years ago
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    The first inequality, I went ahead and said 10^2 instead of (-10)^2 since 10^2 is the same result at (-10)^2.

  12. sinusoidal
    • 2 years ago
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    right, I get it now. I wasn't thinking about getting rid of the inequalities and just replacing them back at the end. it makes the process a lot simpler

  13. sinusoidal
    • 2 years ago
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    and I was thrown off by the complex solution too

  14. sinusoidal
    • 2 years ago
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    thanks

  15. myininaya
    • 2 years ago
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    Np. Have fun. :)

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