powers!!!!

Number Theory Level 4

Question no3

If α , β , γ \alpha,\beta,\gamma are the roots of the equation x 3 + 3 x + 9 = 0 x^{3}+3x+9=0 ,find the value of α 18 + β 18 + γ 18 \alpha^{18}+\beta^{18}+\gamma^{18}

NOTE:This is not a original problem.I just modified it.


The answer is -10668186.

Divyansh Khatri by Divyansh Khatri , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rajen Kapur
Feb 19, 2015

I got the answer by first making a cube, then its square to get a cubic equation for which I found the sum of cubes. Tedious though. I look forward to someone posting a shorter method. Sometime soon I intend to post my solution.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...