let p,q,r,s, and t be roots of x^5-160x-128 = 0. Compute p^5 + q^5 + r^5 + s^5 + t^5
+129838 Here are the roots here......http://www.wolframalpha.com/input/?i=solve+x^5++-160x+-128+%3D+0
Just assign each "real" root to a different variable, take the 5th power of each, and sum your answers.
P.S. (The sum of the non-real roots raised to the 5th power is about 160 .....it actually may be 160 exactly....I used Wolfram Alpha to find the roots....and they may have been "rounded")
+129838 Here are the roots here......http://www.wolframalpha.com/input/?i=solve+x^5++-160x+-128+%3D+0
Just assign each "real" root to a different variable, take the 5th power of each, and sum your answers.
P.S. (The sum of the non-real roots raised to the 5th power is about 160 .....it actually may be 160 exactly....I used Wolfram Alpha to find the roots....and they may have been "rounded")
+33653 Because x5 = 160x + 128 the sum of the fifth powers of the five roots will be 160*(p+q+r+s+t) + 5*128
Numerically, the p+q+r+s+t seems to be 0 (I used Mathcad's symbolic calculator with 200 significant figures and got a number around 10-204 for the sum). If so then the sum p5+q5+r5+s5+t5 = 5*128 = 640.
