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Why the roots of Eq. x^2 + a*x + b = 0

  1. Aug 9, 2011 #1
    Why the roots of Eq. x^2 + a*x + b = 0 and of Eq. x + a*Sqrt[x] + b = 0 are not identically? How can I expand the second Eq. in simple fractions: x + a*Sqrt[x] + b = ... ?
    Thank you. Lucas
  2. jcsd
  3. Aug 9, 2011 #2
    Re: Roots

    Because they are different equations! In the second equation, you can substitute [itex]y=\sqrt{x}[/itex] and it becomes [itex]y^2+ay+b=0[/itex]. Now the solution to the second equation is the same as the solution of the first, but remember that the solution we've got for the second equation is [itex]y[/itex], not [itex]x[/itex]! To find [itex]x[/itex], you have to square the solution you've got, and the solutions are different.
  4. Aug 9, 2011 #3


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    Science Advisor

    Re: Roots

    Now, what do you mean by "expand in simple fractions"?
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