|x+1/x |=3

解

x + \frac{1}{x} = 3

x = \frac{- 3 - 5}{2} or x = \frac{- 3 + 5}{2} or x = \frac{3 - 5}{2} or x = \frac{3 + 5}{2}

十進法表記

x = - 2.61803 \dots, x = - 0.38196 \dots, x = 0.38196 \dots, x = 2.61803 \dots

解答ステップ

x + \frac{1}{x} = 3

絶対規則を適用する:

∣ u ∣ = a, a > 0

の場合は

u = a

u = - a

x + \frac{1}{x} = - 3 or x + \frac{1}{x} = 3

x + \frac{1}{x} = - 3 or x + \frac{1}{x} = 3

(x = \frac{- 3 - 5}{2} or x = \frac{- 3 + 5}{2}) or (x = \frac{3 - 5}{2} or x = \frac{3 + 5}{2})

x = \frac{- 3 - 5}{2} or x = \frac{- 3 + 5}{2} or x = \frac{3 - 5}{2} or x = \frac{3 + 5}{2}