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人気のある代数 >

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

解

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

解

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

equationを

u = x^{3}

と以下で書き換える:

u^{2} = x^{6}

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^{3}

に置き換えて以下を解く:

x

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 = 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} = x^{5}

(2 x + 1)^{3} = 900

11x^{10}-60x^9=0

11 x^{10} - 60 x^{9} = 0

-x^3+0.8x^2+0.260625x-0.08775=0

- x^{3} + 0.8 x^{2} + 0.260625 x - 0.08775 = 0

因数 4x^3-120x^2+864x-1820=0

f a c t or 4 x^{3} - 120 x^{2} + 864 x - 1820 = 0