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人気のある代数 >

-50-w(w^3-9w)=0

解

- 50 - w (w^{3} - 9 w) = 0

解

w = \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i

解答ステップ

- 50 - w (w^{3} - 9 w) = 0

拡張

- 50 - w (w^{3} - 9 w) : - 50 - w^{4} + 9 w^{2}

- 50 - w^{4} + 9 w^{2} = 0

標準的な形式で書く

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- w^{4} + 9 w^{2} - 50 = 0

equationを

u = w^{2}

と以下で書き換える:

u^{2} = w^{4}

- u^{2} + 9 u - 50 = 0

解く

- u^{2} + 9 u - 50 = 0 : u = \frac{9}{2} - i \frac{119}{2}, u = \frac{9}{2} + i \frac{119}{2}

u = \frac{9}{2} - i \frac{119}{2}, u = \frac{9}{2} + i \frac{119}{2}

再び

u = w^{2}

に置き換えて以下を解く:

w

解く

w^{2} = \frac{9}{2} - i \frac{119}{2} : w = \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i

解く

w^{2} = \frac{9}{2} + i \frac{119}{2} : w = \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i

解答は

w = \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = \frac{9 + 10 2}{2} + \frac{119}{2 9 + 10 2} i, w = - \frac{9 + 10 2}{2} - \frac{119}{2 9 + 10 2} i

グラフ

人気の例

-λ^3+10λ^2-33λ+36=0

- λ^{3} + 10 λ^{2} - 33 λ + 36 = 0

0=-4x^3+2x^2+x-2

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

2s^4+48s^2-50=0

2 s^{4} + 48 s^{2} - 50 = 0

x^3+4x^2-10x-40=0

x^{3} + 4 x^{2} - 10 x - 40 = 0

2x^3+10x^2+4x=-8x

2 x^{3} + 10 x^{2} + 4 x = - 8 x