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受欢迎的代数 >

r^9g+9-12g=19g+9

解答

r^{9} g + 9 - 12 g = 19 g + 9

解答

r = 3331, r = - 3331 \frac{1}{2} + 3331 \frac{3}{2} i, r = - 3331 \frac{1}{2} - 3331 \frac{3}{2} i, r = cos (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{8 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{14 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{4 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{10 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 1^{\frac{2}{3}}

求解步骤

r^{9} g + 9 - 12 g = 19 g + 9

将

12 g

到右边

r^{9} g + 9 = 31 g + 9

将

9

到右边

r^{9} g = 31 g

两边除以

g; g \neq = 0

r^{9} = 31; g \neq = 0

用

u = r^{3}

和

u^{3} = r^{9}

改写方程式

u^{3} = 31

解

u^{3} = 31 : u = 331, u = 331 \frac{- 1 + 3 i}{2}, u = 331 \frac{- 1 - 3 i}{2}

u = 331, u = 331 \frac{- 1 + 3 i}{2}, u = 331 \frac{- 1 - 3 i}{2}

代回

u = r^{3}

，求解

r

解

r^{3} = 331 : r = 3331, r = - 3331 \frac{1}{2} + 3331 \frac{3}{2} i, r = - 3331 \frac{1}{2} - 3331 \frac{3}{2} i

解

r^{3} = 331 \frac{- 1 + 3 i}{2} : r = cos (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{8 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{14 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 1^{\frac{2}{3}}

解

r^{3} = 331 \frac{- 1 - 3 i}{2} : r = cos (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{4 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{10 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 1^{\frac{2}{3}}

解为

r = 3331, r = - 3331 \frac{1}{2} + 3331 \frac{3}{2} i, r = - 3331 \frac{1}{2} - 3331 \frac{3}{2} i, r = cos (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{8 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{14 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{4 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 1^{\frac{2}{3}}, r = cos (\frac{10 π}{9}) 6 3 1^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 1^{\frac{2}{3}}

作图

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