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受欢迎的代数 >

x^6-x^3+1=0

解答

x^{6} - x^{3} + 1 = 0

解答

x = cos (\frac{π}{9}) + i sin (\frac{π}{9}), x = cos (\frac{7 π}{9}) + i sin (\frac{7 π}{9}), x = cos (\frac{13 π}{9}) + i sin (\frac{13 π}{9}), x = cos (\frac{π}{9}) - i sin (\frac{π}{9}), x = cos (\frac{5 π}{9}) + i sin (\frac{5 π}{9}), x = cos (\frac{11 π}{9}) + i sin (\frac{11 π}{9})

求解步骤

x^{6} - x^{3} + 1 = 0

用

u = x^{3}

和

u^{2} = x^{6}

改写方程式

u^{2} - u + 1 = 0

解

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

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

代回

u = x^{3}

，求解

x

解

x^{3} = \frac{1}{2} + i \frac{3}{2} : x = cos (\frac{π}{9}) + i sin (\frac{π}{9}), x = cos (\frac{7 π}{9}) + i sin (\frac{7 π}{9}), x = cos (\frac{13 π}{9}) + i sin (\frac{13 π}{9})

解

x^{3} = \frac{1}{2} - i \frac{3}{2} : x = cos (\frac{π}{9}) - i sin (\frac{π}{9}), x = cos (\frac{5 π}{9}) + i sin (\frac{5 π}{9}), x = cos (\frac{11 π}{9}) + i sin (\frac{11 π}{9})

解为

x = cos (\frac{π}{9}) + i sin (\frac{π}{9}), x = cos (\frac{7 π}{9}) + i sin (\frac{7 π}{9}), x = cos (\frac{13 π}{9}) + i sin (\frac{13 π}{9}), x = cos (\frac{π}{9}) - i sin (\frac{π}{9}), x = cos (\frac{5 π}{9}) + i sin (\frac{5 π}{9}), x = cos (\frac{11 π}{9}) + i sin (\frac{11 π}{9})

作图

流行的例子

z^4=8sqrt(2)+8sqrt(2)i

z^{4} = 82 + 82 i

x^3-7x^2+4x+30=0

x^{3} - 7 x^{2} + 4 x + 30 = 0

(x)=x^3-3x^2-9x-5

(x) = x^{3} - 3 x^{2} - 9 x - 5

solvefor x,x^2+(y-cbrt(x^2))^2=25

so l v e f or x, x^{2} + (y - c b r t (x^{2}))^{2} = 25

根 z^4-3z^3-5z^2+6z-8

roo t s z^{4} - 3 z^{3} - 5 z^{2} + 6 z - 8