Jika x + x^-1 = 3 Maka tentukan a. X^2+x^-2 B. X^3 + x^-3 C. X^4 + x^-4 D. X^5 + x^-5

kedua ruas kuadrat kan
a) (x¹ + x^-1)² = 3²
x² + 2 + x^-2 = 9
x² + x^-2 = 9-2
x² + x^-2 = 7

b) (x^1 + x^-1)(x^2 + x^-2) = (3)(9)
x^3 + x^1 + x^-1 + x^-3 = 27
x^3 + 3 + x^-3 = 27
x^3 + x^-3 = 27-3 = 24

c) (x^2 + x^-2)² = 7²
x^4 + 2 + x^-4 = 49
x^4 + x^-4 = 49 - 2 = 47

d) (x^3 + x^-3)(x^2 + x^-2) = (24)(7)
x^5 + x^1 + x^-1 + x^5 = 168
x^5 + 3 + x^-5 = 168
x^5 + x^-5 = 168 - 3 = 165