Question

Jika x + 1/x = 1,berapakah hasil dari +1/

Answer 1

X + 1/x = 1

kuadratkan kedua ruas, get
x^2 + 2 + 1/x^2 = 1
x^2 + 1/x^2 = -1

kuadratkan kedua ruas lagi, get
x^4 + 2 + 1/x^4 = 1
x^4 + 1/x^4 = -1

kuadratkan kedua ruas lagi, get
x^8 + 2 + x^8 = 1
x^8 + 1/x^8 = -1

perhatikan bahwa :
(x^4 + 1/x^4)(x^8 + 1/x^8) = (-1) * (-1)
x^12 + 1/x^12 + x^4 + 1/x^4 = 1
x^12 + 1/x^12 - 1 = 1
(x^12 + 1/x^12) = 2

terakhir, expand :
(x^8 + 1/x^8)(x^12 + 1/x^12) = -1 * 2
x^20 + 1/x^20 + x^4 + 1/x^4 = -2
x^20 + 1/x^20 - 1 = -2
x^20 + 1/x^20 = -2 + 1
x^20 + 1/x^20 = -1