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A problem in Quadratic Equations

  1. May 18, 2017 #1
    • Member warned that some effort must be shown
    1. The problem statement, all variables and given/known data

    Find the number of solutions of the equation $$\sqrt {x^2}-\sqrt {(x-1)^2} + \sqrt {(x-2)^2}=\sqrt {5}$$
    Answer given: 2

    2. Relevant equations

    3. The attempt at a solution

    Completely clueless as to where to start.
     
    Last edited: May 18, 2017
  2. jcsd
  3. May 18, 2017 #2

    ehild

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    What is the square root of the square of a number ? ##\sqrt{a^2} = ?##
     
    Last edited: May 18, 2017
  4. May 22, 2017 #3

    ehild

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    Write the equation without square roots and squares. Do you know what is ##\sqrt{3^2}##? and ##\sqrt{(-3)^2}##? And what is ##\sqrt{a^2}## in general?
     
  5. May 22, 2017 #4
    ##\sqrt{a^2} = |a|##, that much I know. And the others are both 3.
     
  6. May 22, 2017 #5
    You mean to say that the expression reduces to ## |x|-|x-1|+|x-2|=\sqrt {5}##?

    Then I can solve it without problem, just tell if my evaluation is correct.
     
  7. May 22, 2017 #6

    ehild

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    Yes, it is correct. Just plot the function, and see, if it can take the value √5, and how many times.
     
  8. May 22, 2017 #7
    Right, plot on a number line and... I understood. Thank you, sir. :partytime:
     
  9. May 22, 2017 #8

    ehild

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    Well, this is the plot

    upload_2017-5-22_23-27-0.png
     
    Last edited: May 22, 2017
  10. May 23, 2017 #9
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