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人気のある代数 >

15X^4-445X^2+8000=0

解

15 X^{4} - 445 X^{2} + 8000 = 0

解

X = \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i

解答ステップ

15 X^{4} - 445 X^{2} + 8000 = 0

equationを

u = X^{2}

と以下で書き換える:

u^{2} = X^{4}

15 u^{2} - 445 u + 8000 = 0

解く

15 u^{2} - 445 u + 8000 = 0 : u = \frac{89}{6} + i \frac{11279}{6}, u = \frac{89}{6} - i \frac{11279}{6}

u = \frac{89}{6} + i \frac{11279}{6}, u = \frac{89}{6} - i \frac{11279}{6}

再び

u = X^{2}

に置き換えて以下を解く:

X

解く

X^{2} = \frac{89}{6} + i \frac{11279}{6} : X = \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i

解く

X^{2} = \frac{89}{6} - i \frac{11279}{6} : X = \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i

解答は

X = \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i

グラフ

人気の例

4 x - 4 x^{6} = 0

4X+X^4+9X+18=12(X+2)

4 X + X^{4} + 9 X + 18 = 12 (X + 2)

(1 + x)^{12} = 1.1

x^{3} + 5 x^{2} - 24 x = 0

x^3+3x^2+2x+1.06=0

x^{3} + 3 x^{2} + 2 x + 1.06 = 0