Tough problem.
Evaluate a^3 + 1/(a^3) if a + 1/a = 6
Tell me if anything is unclear.
+128406
a^3 + 1/a^3 if a + 1/a = 6
Note that (a + 1/a)^2 = a^2 + 2 + 1/a^2 = 36 → a^2 + 1/a^2 = 34
And a^3 + 1/a^3 can be factored as a sum of cubes thusly
(a + 1/a) ( a^2 - 1 + 1/a^2) =
(6) ([ a^2 + 1/a^2] - 1 ) =
(6) ( 34 - 1 ) =
6 * 33=
198
P.S. - thanks to hectictar for spotting my earlier error...!!!!
