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人気のある代数 >

0=x^4+x^2+1

解

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

解

x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

解答ステップ

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

辺を交換する

x^{4} + x^{2} + 1 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

u^{2} + u + 1 = 0

解く

u^{2} + u + 1 = 0 : u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

u = - \frac{1}{2} + i \frac{3}{2}, u = - \frac{1}{2} - i \frac{3}{2}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = - \frac{1}{2} + i \frac{3}{2} : x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

解く

x^{2} = - \frac{1}{2} - i \frac{3}{2} : x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

解答は

x = \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} - \frac{3}{2} i, x = - \frac{1}{2} + \frac{3}{2} i

グラフ

人気の例

solvefor r,A=4rpir^2

so l v e f or r, A = 4 r π r^{2}

4 x^{2} 11 x - 3 = 0

x^3+6x^2-2x-12=0

x^{3} + 6 x^{2} - 2 x - 12 = 0

x^4+7x^3+5x^2-31x-30=0

x^{4} + 7 x^{3} + 5 x^{2} - 31 x - 30 = 0

x^3+9x^2=4x^2-x-5

x^{3} + 9 x^{2} = 4 x^{2} - x - 5