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

1. Jan 23, 2013

### chloe1995

1. The problem statement, all variables and given/known data

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

$25x^2-5\sqrt{76}x+15=0$

2. Relevant equations
3. The attempt at a solution

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

What can I do afterwards that does not constitute as solving the equation? Thanks.

2. Jan 23, 2013

### SteamKing

Staff Emeritus
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.

3. Jan 23, 2013

### SammyS

Staff Emeritus
Hello chloe1995. Welcome to PF !

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

Then $\displaystyle \ \ x_1 + x_2 = -\frac{b}{a}\ \$ and $\displaystyle \ \ x_1\cdot x_2=\frac{c}{a}\ .\$

4. Jan 23, 2013

### chloe1995

Oops! I meant completing the square.

Thank you.

5. Jan 23, 2013

### SammyS

Staff Emeritus
So, Have you managed to solve the problem?