Question

Diketahui x^2 + x^-2 = 3 dan x^4 - x^-4 = 5. Tentukan nilai x^8 -x^-8.

Answer 1

P = x^2
q = x^-2
p. q =1
p+q = 3
p^2 - q^2 = 5
p^2 + q^2 = (p+q)^2 - 2pq = 3^2 - 2(1) = 7
.
p^2 = x^4
q^2 = x^-4
.
p^4 = x^8
q^4 = x^-8
.
x^8 - x^-8 = p^4 - q^4
x^8 - x^-8 = (p^2 +q^2) (p^2 - q^2)
 x^8 - x^-8=  (7)(5)= 35 
.