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受欢迎的代数 >

81=1.5^2× x^9

解答

81 = 1. 5^{2} \cdot x^{9}

解答

x = 3336, x = - 3336 \frac{1}{2} + 3336 \frac{3}{2} i, x = - 3336 \frac{1}{2} - 3336 \frac{3}{2} i, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}}

求解步骤

81 = 1. 5^{2} x^{9}

交换两边

1. 5^{2} x^{9} = 81

两边除以

2.25

x^{9} = 36

用

u = x^{3}

和

u^{3} = x^{9}

改写方程式

u^{3} = 36

解

u^{3} = 36 : u = 336, u = 336 \frac{- 1 + 3 i}{2}, u = 336 \frac{- 1 - 3 i}{2}

u = 336, u = 336 \frac{- 1 + 3 i}{2}, u = 336 \frac{- 1 - 3 i}{2}

代回

u = x^{3}

，求解

x

解

x^{3} = 336 : x = 3336, x = - 3336 \frac{1}{2} + 3336 \frac{3}{2} i, x = - 3336 \frac{1}{2} - 3336 \frac{3}{2} i

解

x^{3} = 336 \frac{- 1 + 3 i}{2} : x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}}

解

x^{3} = 336 \frac{- 1 - 3 i}{2} : x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}}

解为

x = 3336, x = - 3336 \frac{1}{2} + 3336 \frac{3}{2} i, x = - 3336 \frac{1}{2} - 3336 \frac{3}{2} i, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}}

作图

流行的例子

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