2(x-[ 1/x ])^2+3(x+[ 1/x ])-12=0

解

2 (x - [\frac{1}{x}])^{2} + 3 (x + [\frac{1}{x}]) - 12 = 0

x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

十進法表記

x = 2, x = 0.5, x = - 0.26794 \dots, x = - 3.73205 \dots

解答ステップ

2 (x - [\frac{1}{x}])^{2} + 3 (x + [\frac{1}{x}]) - 12 = 0

LCMで乗じる

2 x^{4} + 3 x^{3} + 2 + 3 x - 16 x^{2} = 0

解く

2 x^{4} + 3 x^{3} + 2 + 3 x - 16 x^{2} = 0 : x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3

解を検算する

未定義の (特異) 点を求める:

x = 0

未定義のポイントを解に組み合わせる:

x = 2, x = \frac{1}{2}, x = - 2 + 3, x = - 2 - 3