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受欢迎的代数 >

10x^9=7x

解答

10 x^{9} = 7 x

解答

x = 0, x = - 8 \frac{7}{10}, x = 8 \frac{7}{10}, x = - 4 \frac{7}{10}, x = - - 4 \frac{7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

求解步骤

10 x^{9} = 7 x

将

7 x

para o lado esquerdo

10 x^{9} - 7 x = 0

因式分解

10 x^{9} - 7 x : x (810 x + 87) (810 x - 87) (410 x^{2} + 47) (410 x^{2} + 2^{\frac{5}{8}} 835 x + 47) (410 x^{2} - 2^{\frac{5}{8}} 835 x + 47)

x (810 x + 87) (810 x - 87) (410 x^{2} + 47) (410 x^{2} + 2^{\frac{5}{8}} 835 x + 47) (410 x^{2} - 2^{\frac{5}{8}} 835 x + 47) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 810 x + 87 = 0 or 810 x - 87 = 0 or 410 x^{2} + 47 = 0 or 410 x^{2} + 2^{\frac{5}{8}} 835 x + 47 = 0 or 410 x^{2} - 2^{\frac{5}{8}} 835 x + 47 = 0

解

810 x + 87 = 0 : x = - 8 \frac{7}{10}

解

810 x - 87 = 0 : x = 8 \frac{7}{10}

解

410 x^{2} + 47 = 0 : x = - 4 \frac{7}{10}, x = - - 4 \frac{7}{10}

解

410 x^{2} + 2^{\frac{5}{8}} 835 x + 47 = 0 : x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

解

410 x^{2} - 2^{\frac{5}{8}} 835 x + 47 = 0 : x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

解为

x = 0, x = - 8 \frac{7}{10}, x = 8 \frac{7}{10}, x = - 4 \frac{7}{10}, x = - - 4 \frac{7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

作图

流行的例子

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