Question

If a+ 1/a =4, prove that prove that a ^ 2 + 1/(a ^ 2) = 14; and a ^ 4 + 1/(a ^ 4) = 194 .

*PLEASE HELP*​

Answer 1

Answer:

(a^2 + 1/(a^2) + 2) = 16. (a^2 + 1/(a^2)) = 14.

(a^4 + 1/(a^4) + 2) = 196. (a^4 + 1/(a^4)) = 194.

In the general case, where (a + 1/a) = n , and n an integer, (a^2 + 1/(a^2)) = (n^2 - 2).

(a^4 + 1/(a^4)) = (n^2 - 2)^2 - 2 = (n^4 - 4n^2 + 2 ).