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人気のある代数 >

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

解

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

解

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

解答ステップ

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

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

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

解く

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

u = 1 + 2 i, u = 1 - 2 i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

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

解く

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

解答は

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

グラフ

人気の例

solvefor a,a^5+b^5=4806

so l v e f or a, a^{5} + b^{5} = 4806

5 x^{3} = 45 x

x^3+3x^2+4x-11=0

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

x^3-18*x^2+81*x-108=0

x^{3} - 18 \cdot x^{2} + 81 \cdot x - 108 = 0

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

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