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人気のある代数 >

5x^4+15x^2+50=0

解

5 x^{4} + 15 x^{2} + 50 = 0

解

x = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

解答ステップ

5 x^{4} + 15 x^{2} + 50 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

5 u^{2} + 15 u + 50 = 0

解く

5 u^{2} + 15 u + 50 = 0 : u = - \frac{3}{2} + i \frac{31}{2}, u = - \frac{3}{2} - i \frac{31}{2}

u = - \frac{3}{2} + i \frac{31}{2}, u = - \frac{3}{2} - i \frac{31}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = - \frac{3}{2} + i \frac{31}{2} : x = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i

解く

x^{2} = - \frac{3}{2} - i \frac{31}{2} : x = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

解答は

x = \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = \frac{- 3 + 2 10}{2} - \frac{31}{2 - 3 + 2 10} i, x = - \frac{- 3 + 2 10}{2} + \frac{31}{2 - 3 + 2 10} i

グラフ

人気の例

3x^3-3x^2-7x+5=x^3-2x^2-1

3 x^{3} - 3 x^{2} - 7 x + 5 = x^{3} - 2 x^{2} - 1

0.75=10x^9-9x^{10}

0.75 = 10 x^{9} - 9 x^{10}

4 x^{3} - 9 x^{2} + 4 = 0

-x^3+2x^2+7x+4=0

- x^{3} + 2 x^{2} + 7 x + 4 = 0

3x^3+4x^2-9x-12=0

3 x^{3} + 4 x^{2} - 9 x - 12 = 0