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人気のある代数 >

(x+1/x)^2=3^2

解

(x + \frac{1}{x})^{2} = 3^{2}

解

x = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

+1

十進法表記

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

解答ステップ

(x + \frac{1}{x})^{2} = 3^{2}

簡素化

(x + \frac{1}{x})^{2} : x^{2} + 2 + \frac{1}{x ^{2}}

x^{2} + 2 + \frac{1}{x ^{2}} = 3^{2}

以下で両辺を乗じる:

x^{2}

x^{4} + 2 x^{2} + 1 = 9 x^{2}

解く

x^{4} + 2 x^{2} + 1 = 9 x^{2} : x = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

x = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

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 = \frac{7 + 3 5}{2}, x = - \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}, x = - \frac{7 - 3 5}{2}

グラフ

人気の例

(3(7x+13))/(12x+15)=2

\frac{3 ( 7 x + 13 )}{12 x + 15} = 2

(24)/(3+2x-8)=27+13

\frac{24}{3 + 2 x - 8} = 27 + 13

4+6/(x-5)= 2/(x-5)

4 + \frac{6}{x - 5} = \frac{2}{x - 5}

(-4)/(x-4)=1-2/(x+8)

\frac{- 4}{x - 4} = 1 - \frac{2}{x + 8}

x/((x+3)(x+1))=0

\frac{x}{( x + 3 ) ( x + 1 )} = 0