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人気のある代数 >

x^3-3=x^9+3

解

x^{3} - 3 = x^{9} + 3

解

x = - 32, x = \frac{3 2}{2} - i \frac{3 2 3}{2}, x = \frac{3 2}{2} + i \frac{3 2 3}{2}, x = 63 cos (\frac{arctan ( 2 )}{3}) + 63 i sin (\frac{arctan ( 2 )}{3}), x = 63 cos (\frac{arctan ( 2 ) + 2 π}{3}) + 63 i sin (\frac{arctan ( 2 ) + 2 π}{3}), x = 63 cos (\frac{arctan ( 2 ) + 4 π}{3}) + 63 i sin (\frac{arctan ( 2 ) + 4 π}{3}), x = 63 cos (\frac{arctan ( 2 )}{3}) - 63 i sin (\frac{arctan ( 2 )}{3}), x = 63 cos (\frac{- arctan ( 2 ) + 2 π}{3}) + 63 i sin (\frac{- arctan ( 2 ) + 2 π}{3}), x = 63 cos (\frac{- arctan ( 2 ) + 4 π}{3}) + 63 i sin (\frac{- arctan ( 2 ) + 4 π}{3})

解答ステップ

x^{3} - 3 = x^{9} + 3

辺を交換する

x^{9} + 3 = x^{3} - 3

3

を左側に移動します

x^{9} + 6 = x^{3}

x^{3}

を左側に移動します

x^{9} + 6 - x^{3} = 0

標準的な形式で書く

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

x^{9} - x^{3} + 6 = 0

equationを

u = x^{3}

と以下で書き換える:

u^{3} = x^{9}

u^{3} - u + 6 = 0

解く

u^{3} - u + 6 = 0 : u = - 2, u = 1 + 2 i, u = 1 - 2 i

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

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = - 2 : x = - 32, x = \frac{3 2}{2} - i \frac{3 2 3}{2}, x = \frac{3 2}{2} + i \frac{3 2 3}{2}

解く

x^{3} = 1 + 2 i : x = 63 cos (\frac{arctan ( 2 )}{3}) + 63 i sin (\frac{arctan ( 2 )}{3}), x = 63 cos (\frac{arctan ( 2 ) + 2 π}{3}) + 63 i sin (\frac{arctan ( 2 ) + 2 π}{3}), x = 63 cos (\frac{arctan ( 2 ) + 4 π}{3}) + 63 i sin (\frac{arctan ( 2 ) + 4 π}{3})

解く

x^{3} = 1 - 2 i : x = 63 cos (\frac{arctan ( 2 )}{3}) - 63 i sin (\frac{arctan ( 2 )}{3}), x = 63 cos (\frac{- arctan ( 2 ) + 2 π}{3}) + 63 i sin (\frac{- arctan ( 2 ) + 2 π}{3}), x = 63 cos (\frac{- arctan ( 2 ) + 4 π}{3}) + 63 i sin (\frac{- arctan ( 2 ) + 4 π}{3})

解答は

x = - 32, x = \frac{3 2}{2} - i \frac{3 2 3}{2}, x = \frac{3 2}{2} + i \frac{3 2 3}{2}, x = 63 cos (\frac{arctan ( 2 )}{3}) + 63 i sin (\frac{arctan ( 2 )}{3}), x = 63 cos (\frac{arctan ( 2 ) + 2 π}{3}) + 63 i sin (\frac{arctan ( 2 ) + 2 π}{3}), x = 63 cos (\frac{arctan ( 2 ) + 4 π}{3}) + 63 i sin (\frac{arctan ( 2 ) + 4 π}{3}), x = 63 cos (\frac{arctan ( 2 )}{3}) - 63 i sin (\frac{arctan ( 2 )}{3}), x = 63 cos (\frac{- arctan ( 2 ) + 2 π}{3}) + 63 i sin (\frac{- arctan ( 2 ) + 2 π}{3}), x = 63 cos (\frac{- arctan ( 2 ) + 4 π}{3}) + 63 i sin (\frac{- arctan ( 2 ) + 4 π}{3})

グラフ

人気の例

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

y^{3} + 27 = 0

(2 a)^{3} = 2 a^{3}

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

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

0=2x^9-3x^7+11x+10

0 = 2 x^{9} - 3 x^{7} + 11 x + 10