tolong kakak.... di bantu soal JMO 2007

kuadratkan kedua ruas
(x + 1/x)² = 1²
x² + 2 + 1/x² = 1
x² + 1/x² = -1
kuadratkan lagi
(x² + 1/x²)² = -1²
x⁴ + 2 + 1/x⁴ = 1
x⁴ + 1/x⁴ = -1

(x⁴ + 1/x⁴) = -1²
x^8 + 2 + 1/x^8 = 1
x^8 + 1/x^8 = -1

(x⁴ + 1/x⁴)(x² + 1/x²) = (-1)(-1)
x^6 + x² + 1/x² + 1/x^6 = 1
x^6 + (x² + 1/x²) + 1/x^6 = 1
x^6 + (-1) + 1/x^6 = 1
x^6 + 1/x^6 = 2

(x^8 + 1/x^8)(x² + 1/x²) = (-1)(-1)
x^10 + x^6 + 1/x^6 + 1/x^10 = 1
x^10 + (x^6 + 1/x^6) + 1/x^10 = 1
x^10 + (2) + 1/x^10 = 1
x^10 + 1/x^10 = -1

sampe sini ajah kayanya bisanya coba perhatiin dulu bener gak