Réponse:
(x+1/x)²=x²=1/x²+2(x)(1/x)
(17/4) ^ 2 = x ^ 2 + 1 / (x ^ 2) + 2
289/16 - 2 = x ^ 2 + 1 / (x ^ 2)
by taking LCM
(289 - 32) / 16 = x ^ 2 + 1 / (x ^ 2)
257/16 = x ^ 2 + 1 / (x ^ 2)
now
(x - 1 / x) ^ 2 = x ^ 2 + 1 / (x ^ 2) - 2
(x-1/x)²=257/16-2
(x - 1 / x) ^ 2 = (257 - 32) / 16
(x - 1 / x) ^ 2 = 225/16
(x - 1 / x) = 15/4