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受欢迎的代数 >

28a^{12}=56a^{15}

解答

28 a^{12} = 56 a^{15}

解答

a = 0, a = \frac{1}{3 2}, a = - \frac{2 ^{\frac{2}{3}}}{4} + i \frac{3 2 3 2 ^{\frac{2}{3}}}{4}, a = - \frac{2 ^{\frac{2}{3}}}{4} - i \frac{3 2 3 2 ^{\frac{2}{3}}}{4}

求解步骤

28 a^{12} = 56 a^{15}

将

56 a^{15}

para o lado esquerdo

28 a^{12} - 56 a^{15} = 0

因式分解

28 a^{12} - 56 a^{15} : - 28 a^{12} (32 a - 1) (2^{\frac{2}{3}} a^{2} + 32 a + 1)

- 28 a^{12} (32 a - 1) (2^{\frac{2}{3}} a^{2} + 32 a + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

a = 0 or 32 a - 1 = 0 or 2^{\frac{2}{3}} a^{2} + 32 a + 1 = 0

解

32 a - 1 = 0 : a = \frac{1}{3 2}

解

2^{\frac{2}{3}} a^{2} + 32 a + 1 = 0 : a = - \frac{2 ^{\frac{2}{3}}}{4} + i \frac{3 2 3 2 ^{\frac{2}{3}}}{4}, a = - \frac{2 ^{\frac{2}{3}}}{4} - i \frac{3 2 3 2 ^{\frac{2}{3}}}{4}

解为

a = 0, a = \frac{1}{3 2}, a = - \frac{2 ^{\frac{2}{3}}}{4} + i \frac{3 2 3 2 ^{\frac{2}{3}}}{4}, a = - \frac{2 ^{\frac{2}{3}}}{4} - i \frac{3 2 3 2 ^{\frac{2}{3}}}{4}

作图

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