Lim (5p + 7p + 11p)1/p = t3 - t + 5
p→∞

The limit as p approaches infinity for (5^p + 7^p + 11^p)^1/p is 11.

11 = t³ - t + 5 can be rewritten as the cubic equation:
                                 t³ - t - 6 = 0

Solving the cubic equation for t, we get the roots
                           (2, -1+i*2^1/2, -1-i*2^1/2).

Thus, all possible real t that satisfy the equation is {2}.

Edited on February 9, 2008, 10:07 pm

Posted by Dej Mar on 2008-02-09 21:42:01