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受欢迎的代数 >

(4x-1)(5x^3-8.64)=0

解答

(4 x - 1) (5 x^{3} - 8.64) = 0

解答

x = \frac{1}{4}, x = 1.2, x = - \frac{3.50882 \dots}{5.84803 \dots} + i \frac{36.93548 \dots}{5.84803 \dots}, x = - \frac{3.50882 \dots}{5.84803 \dots} - i \frac{36.93548 \dots}{5.84803 \dots}

求解步骤

(4 x - 1) (5 x^{3} - 8.64) = 0

因式分解

(4 x - 1) (5 x^{3} - 8.64) : (4 x - 1) (35 x - 3 8.64) (5^{\frac{2}{3}} x^{2} + 3 43.2 x + 8.6 4^{\frac{2}{3}})

(4 x - 1) (35 x - 3 8.64) (5^{\frac{2}{3}} x^{2} + 3 43.2 x + 8.6 4^{\frac{2}{3}}) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

4 x - 1 = 0 or 35 x - 3 8.64 = 0 or 5^{\frac{2}{3}} x^{2} + 3 43.2 x + 8.6 4^{\frac{2}{3}} = 0

解

4 x - 1 = 0 : x = \frac{1}{4}

解

35 x - 3 8.64 = 0 : x = 1.2

解

5^{\frac{2}{3}} x^{2} + 3 43.2 x + 8.6 4^{\frac{2}{3}} = 0 : x = - \frac{3.50882 \dots}{5.84803 \dots} + i \frac{36.93548 \dots}{5.84803 \dots}, x = - \frac{3.50882 \dots}{5.84803 \dots} - i \frac{36.93548 \dots}{5.84803 \dots}

解为

x = \frac{1}{4}, x = 1.2, x = - \frac{3.50882 \dots}{5.84803 \dots} + i \frac{36.93548 \dots}{5.84803 \dots}, x = - \frac{3.50882 \dots}{5.84803 \dots} - i \frac{36.93548 \dots}{5.84803 \dots}

作图

流行的例子

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