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## Homework Statement

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]

## Homework Equations

## 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.