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受欢迎的代数 >

4x^{12}=6

解答

4 x^{12} = 6

解答

x = 6 \frac{3}{2}, x = - 6 \frac{3}{2}, x = - 6 \frac{3}{2}, x = - - 6 \frac{3}{2}, x = 0.89578 \dots + \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = - 0.89578 \dots - \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = - 0.51718 \dots + \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = 0.51718 \dots - \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = 0.51718 \dots + \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = - 0.51718 \dots - \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = - 0.89578 \dots + \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = 0.89578 \dots - \frac{1.14471 \dots - 0.53495 \dots}{2} i

求解步骤

4 x^{12} = 6

两边除以

4

x^{12} = \frac{3}{2}

用

u = x^{2}

和

u^{6} = x^{12}

改写方程式

u^{6} = \frac{3}{2}

解

u^{6} = \frac{3}{2} : u = 3 \frac{3}{2}, u = - 3 \frac{3}{2}, u = \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} + 0.92657 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} - 0.92657 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} + 0.92657 \dots i, u = \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} - 0.92657 \dots i

u = 3 \frac{3}{2}, u = - 3 \frac{3}{2}, u = \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} + 0.92657 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} - 0.92657 \dots i, u = - \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} + 0.92657 \dots i, u = \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} - 0.92657 \dots i

代回

u = x^{2}

，求解

x

解

x^{2} = 3 \frac{3}{2} : x = 6 \frac{3}{2}, x = - 6 \frac{3}{2}

解

x^{2} = - 3 \frac{3}{2} : x = - 6 \frac{3}{2}, x = - - 6 \frac{3}{2}

解

x^{2} = \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} + 0.92657 \dots i : x = 0.89578 \dots + \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = - 0.89578 \dots - \frac{1.14471 \dots - 0.53495 \dots}{2} i

解

x^{2} = - \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} - 0.92657 \dots i : x = - 0.51718 \dots + \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = 0.51718 \dots - \frac{0.53495 \dots + 1.14471 \dots}{2} i

解

x^{2} = - \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} + 0.92657 \dots i : x = 0.51718 \dots + \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = - 0.51718 \dots - \frac{0.53495 \dots + 1.14471 \dots}{2} i

解

x^{2} = \frac{3 ^{\frac{5}{6}}}{2 ^{\frac{7}{3}} \cdot 0.92657 \dots} - 0.92657 \dots i : x = - 0.89578 \dots + \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = 0.89578 \dots - \frac{1.14471 \dots - 0.53495 \dots}{2} i

解为

x = 6 \frac{3}{2}, x = - 6 \frac{3}{2}, x = - 6 \frac{3}{2}, x = - - 6 \frac{3}{2}, x = 0.89578 \dots + \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = - 0.89578 \dots - \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = - 0.51718 \dots + \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = 0.51718 \dots - \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = 0.51718 \dots + \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = - 0.51718 \dots - \frac{0.53495 \dots + 1.14471 \dots}{2} i, x = - 0.89578 \dots + \frac{1.14471 \dots - 0.53495 \dots}{2} i, x = 0.89578 \dots - \frac{1.14471 \dots - 0.53495 \dots}{2} i

作图

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