zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

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

解答

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

解答

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})

求解步骤

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

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

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

解

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

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

代回

u = x^{3}

，求解

x

解

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

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})

解为

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})

作图

流行的例子

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

因式分解 4x^3-120x^2+864x-1820=0

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