x^4+1/(x^4)=47

解

x^{4} + \frac{1}{x ^{4}} = 47

x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}

解答ステップ

x^{4} + \frac{1}{x ^{4}} = 47

以下で両辺を乗じる:

x^{4}

x^{8} + 1 = 47 x^{4}

解く

x^{8} + 1 = 47 x^{4} : x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}

x = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 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 = 4 \frac{47 + 21 5}{2}, x = - 4 \frac{47 + 21 5}{2}, x = i 4 \frac{47 + 21 5}{2}, x = - i 4 \frac{47 + 21 5}{2}, x = 4 \frac{47 - 21 5}{2}, x = - 4 \frac{47 - 21 5}{2}, x = i 4 \frac{47 - 21 5}{2}, x = - i 4 \frac{47 - 21 5}{2}