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受欢迎的代数 >

21494=35000(1+r)^3

解答

21494 = 35000 (1 + r)^{3}

解答

r = \frac{3 10747}{5 3 140} - 1, r = \frac{3 5 ^{\frac{2}{3}} 3 2 ( - 3 10747 - 10 \cdot 2 ^{\frac{2}{3}} 3 35 )}{700} + i \frac{3 5 ^{\frac{2}{3}} 3 11 3 2 3 977 3}{700}, r = \frac{3 5 ^{\frac{2}{3}} 3 2 ( - 3 10747 - 10 \cdot 2 ^{\frac{2}{3}} 3 35 )}{700} - i \frac{3 5 ^{\frac{2}{3}} 3 11 3 2 3 977 3}{700}

求解步骤

21494 = 35000 (1 + r)^{3}

交换两边

35000 (1 + r)^{3} = 21494

两边除以

35000

(1 + r)^{3} = \frac{10747}{17500}

对于

g^{3} (x) = f (a)

解为

g (x) = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

解

1 + r = 3 \frac{10747}{17500} : r = \frac{3 10747}{5 3 140} - 1

解

1 + r = 3 \frac{10747}{17500} \frac{- 1 + 3 i}{2} : r = \frac{3 5 ^{\frac{2}{3}} 3 2 ( - 3 10747 - 10 \cdot 2 ^{\frac{2}{3}} 3 35 )}{700} + i \frac{3 5 ^{\frac{2}{3}} 3 11 3 2 3 977 3}{700}

解

1 + r = 3 \frac{10747}{17500} \frac{- 1 - 3 i}{2} : r = \frac{3 5 ^{\frac{2}{3}} 3 2 ( - 3 10747 - 10 \cdot 2 ^{\frac{2}{3}} 3 35 )}{700} - i \frac{3 5 ^{\frac{2}{3}} 3 11 3 2 3 977 3}{700}

解为

r = \frac{3 10747}{5 3 140} - 1, r = \frac{3 5 ^{\frac{2}{3}} 3 2 ( - 3 10747 - 10 \cdot 2 ^{\frac{2}{3}} 3 35 )}{700} + i \frac{3 5 ^{\frac{2}{3}} 3 11 3 2 3 977 3}{700}, r = \frac{3 5 ^{\frac{2}{3}} 3 2 ( - 3 10747 - 10 \cdot 2 ^{\frac{2}{3}} 3 35 )}{700} - i \frac{3 5 ^{\frac{2}{3}} 3 11 3 2 3 977 3}{700}

作图

流行的例子

x^{4} - 6 x^{2} - 55 = 0

4 x^{3} = 56

4 x^{3} = 40

2 x^{3} - 3 x^{2} + 12 = 0

535 = 5 x^{3}