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Find the value of x1^6 +x2^6 of this quadratic equation without solving itby chloe1995
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#1
Jan2313, 01:25 PM

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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^25\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})^24=0[/itex] What can I do afterwards that does not constitute as solving the equation? Thanks. 


#2
Jan2313, 02:22 PM

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Thanks
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P: 6,477

Notice that 5 can be factored from the quadratic without changing the roots.
Also, you haven't truly factored the quadratic, you have merely rewritten it. 


#3
Jan2313, 03:25 PM

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Suppose that x_{1} and x_{2} 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] 


#4
Jan2313, 08:38 PM

P: 2

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



#5
Jan2313, 09:35 PM

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So, Have you managed to solve the problem?



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