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人気のある代数 >

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

解

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

解

x = \frac{3 + 4 5}{2 2} + \frac{71}{2 2 3 + 4 5} i, x = - \frac{3 + 4 5}{2 2} - \frac{71}{2 2 3 + 4 5} i, x = \frac{3 + 4 5}{2 2} - \frac{71}{2 2 3 + 4 5} i, x = - \frac{3 + 4 5}{2 2} + \frac{71}{2 2 3 + 4 5} i

解答ステップ

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

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

2 u^{2} - 3 u + 10 = 0

解く

2 u^{2} - 3 u + 10 = 0 : u = \frac{3}{4} + i \frac{71}{4}, u = \frac{3}{4} - i \frac{71}{4}

u = \frac{3}{4} + i \frac{71}{4}, u = \frac{3}{4} - i \frac{71}{4}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = \frac{3}{4} + i \frac{71}{4} : x = \frac{3 + 4 5}{2 2} + \frac{71}{2 2 3 + 4 5} i, x = - \frac{3 + 4 5}{2 2} - \frac{71}{2 2 3 + 4 5} i

解く

x^{2} = \frac{3}{4} - i \frac{71}{4} : x = \frac{3 + 4 5}{2 2} - \frac{71}{2 2 3 + 4 5} i, x = - \frac{3 + 4 5}{2 2} + \frac{71}{2 2 3 + 4 5} i

解答は

x = \frac{3 + 4 5}{2 2} + \frac{71}{2 2 3 + 4 5} i, x = - \frac{3 + 4 5}{2 2} - \frac{71}{2 2 3 + 4 5} i, x = \frac{3 + 4 5}{2 2} - \frac{71}{2 2 3 + 4 5} i, x = - \frac{3 + 4 5}{2 2} + \frac{71}{2 2 3 + 4 5} i

グラフ

人気の例

(x^2+3x+2)^2-8(x^2+3x)-4=0

(x^{2} + 3 x + 2)^{2} - 8 (x^{2} + 3 x) - 4 = 0

x^4+3x^3-5x-15=0

x^{4} + 3 x^{3} - 5 x - 15 = 0

solvefor z,z^2(p^2z^2+q^2)=1

so l v e f or z, z^{2} (p^{2} z^{2} + q^{2}) = 1

(x^2-6)(x^2-1)=0

(x^{2} - 6) (x^{2} - 1) = 0

2 x^{4} - 81 = 0