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人気のある代数 >

4*(x^4+1)=5x^2

解

4 \cdot (x^{4} + 1) = 5 x^{2}

解

x = \frac{13}{4} + \frac{3}{4} i, x = - \frac{13}{4} - \frac{3}{4} i, x = \frac{13}{4} - \frac{3}{4} i, x = - \frac{13}{4} + \frac{3}{4} i

解答ステップ

4 (x^{4} + 1) = 5 x^{2}

拡張

4 (x^{4} + 1) : 4 x^{4} + 4

4 x^{4} + 4 = 5 x^{2}

5 x^{2}

を左側に移動します

4 x^{4} + 4 - 5 x^{2} = 0

標準的な形式で書く

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

4 x^{4} - 5 x^{2} + 4 = 0

equationを

u = x^{2}

と以下で書き換える:

u^{2} = x^{4}

4 u^{2} - 5 u + 4 = 0

解く

4 u^{2} - 5 u + 4 = 0 : u = \frac{5}{8} + i \frac{39}{8}, u = \frac{5}{8} - i \frac{39}{8}

u = \frac{5}{8} + i \frac{39}{8}, u = \frac{5}{8} - i \frac{39}{8}

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = \frac{5}{8} + i \frac{39}{8} : x = \frac{13}{4} + \frac{3}{4} i, x = - \frac{13}{4} - \frac{3}{4} i

解く

x^{2} = \frac{5}{8} - i \frac{39}{8} : x = \frac{13}{4} - \frac{3}{4} i, x = - \frac{13}{4} + \frac{3}{4} i

解答は

x = \frac{13}{4} + \frac{3}{4} i, x = - \frac{13}{4} - \frac{3}{4} i, x = \frac{13}{4} - \frac{3}{4} i, x = - \frac{13}{4} + \frac{3}{4} i

グラフ

人気の例

r^3-3r^2+2r-1=0

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