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受欢迎的代数 >

(3x^2)5=3(2x^5)

解答

(3 x^{2}) 5 = 3 (2 x^{5})

解答

x = 0, x = 3 \frac{5}{2}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} + i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} - i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}

求解步骤

(3 x^{2}) \cdot 5 = 3 (2 x^{5})

将

3 (2 x^{5})

para o lado esquerdo

3 x^{2} \cdot 5 - 3 \cdot 2 x^{5} = 0

因式分解

3 x^{2} \cdot 5 - 3 \cdot 2 x^{5} : - 3 x^{2} (32 x - 35) (2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}})

- 3 x^{2} (32 x - 35) (2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}}) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 32 x - 35 = 0 or 2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}} = 0

解

32 x - 35 = 0 : x = 3 \frac{5}{2}

解

2^{\frac{2}{3}} x^{2} + 310 x + 5^{\frac{2}{3}} = 0 : x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} + i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} - i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}

解为

x = 0, x = 3 \frac{5}{2}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} + i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}, x = - \frac{2 ^{\frac{2}{3}} 3 5}{4} - i \frac{3 2 3 1 0 ^{\frac{2}{3}}}{4}

作图

流行的例子

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