Question

MAT

jika x + = 1, tentukan ::
a. +
b. +

Answer 1

X  + 1/x = 1  ... (1)
kuadratkan kedua ruas,
x^2 + 1/x^2 + 2 = 1
x^2 + 1/x^2 = -1  ... (2)
pers (1) x pers (2),
(x + 1/x)(x^2 + 1/x^2) = 1  * -1
x^3 + 1/x^3 + x + 1/x = -1
x^3 + 1/x^3 + 1 = -1
x^3 + 1/x^3 = -2 ... (3)
pers (2) x pers (3),
(x^2 + 1/x^2)(x^3 + 1/x^3) = -1 * -2
x^5 + 1/x^5 + x + 1/x = 2
x^5 + 1/x^5 + 1 = 2
x^5 + 1/x^5 = 1 ... (4)
kuadratkan pers (4),
x^10 + 1/x^10 + 2 = 1
x^10 + 1/x^10 = -1

silahkan diutak-atik untuk soal yg b ......