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Find the value of x1^6 +x2^6 of this quadratic equation without solving it

  1. Jan 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Solve for [itex]x_1^6+x_2^6[/itex] for the following quadratic equation where [itex]x_1[/itex] and [itex]x_2[/itex] are the two real roots and [itex]x_1 > x_2[/itex], without solving the equation.

    [itex]25x^2-5\sqrt{76}x+15=0[/itex]

    2. Relevant equations
    3. The attempt at a solution

    I tried factoring it and I got [itex](-5x+\sqrt{19})^2-4=0[/itex]

    What can I do afterwards that does not constitute as solving the equation? Thanks.
     
  2. jcsd
  3. Jan 23, 2013 #2

    SteamKing

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    Notice that 5 can be factored from the quadratic without changing the roots.

    Also, you haven't truly factored the quadratic, you have merely re-written it.
     
  4. Jan 23, 2013 #3

    SammyS

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    Hello chloe1995. Welcome to PF !

    Suppose that x1 and x2 are the solutions to the quadratic equation, [itex]\displaystyle \ \ ax^2+bx+c=0\ .[/itex]

    Then [itex]\displaystyle \ \ x_1 + x_2 = -\frac{b}{a}\ \ [/itex] and [itex]\displaystyle \ \ x_1\cdot x_2=\frac{c}{a}\ .\ [/itex]
     
  5. Jan 23, 2013 #4
    Oops! I meant completing the square.

    Thank you.
     
  6. Jan 23, 2013 #5

    SammyS

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    So, Have you managed to solve the problem?
     
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