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受欢迎的代数 >

(x^3)/i-27=0

解答

\frac{x ^{3}}{i} - 27 = 0

解答

x = \frac{3 3}{2} + i \frac{3}{2}, x = - \frac{3 3}{2} + i \frac{3}{2}, x = - 3 i

求解步骤

\frac{x ^{3}}{i} - 27 = 0

将

27

到右边

\frac{x ^{3}}{i} = 27

在两边乘以

i

x^{3} = 27 i

For

z^{n} = a

the solutions are

z_{k} = n ∣ a ∣ (cos (\frac{ar g ( a ) + 2 kπ}{n}) + i sin (\frac{ar g ( a ) + 2 kπ}{n})),

k = 0, 1, \dots, n - 1

对于

n = 3, a = 27 i

∣ a ∣ = 27

ar g (a) = \frac{π}{2}

x = 327 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{3})), x = 327 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{3})), x = 327 (cos (\frac{\frac{π}{2} + 2 \cdot 2 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 2 π}{3}))

化简

327 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{3})) : \frac{3 3}{2} + i \frac{3}{2}

化简

327 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{3})) : - \frac{3 3}{2} + i \frac{3}{2}

化简

327 (cos (\frac{\frac{π}{2} + 2 \cdot 2 π}{3}) + i sin (\frac{\frac{π}{2} + 2 \cdot 2 π}{3})) : - 3 i

x = \frac{3 3}{2} + i \frac{3}{2}, x = - \frac{3 3}{2} + i \frac{3}{2}, x = - 3 i

流行的例子

x^2(5x-7)(3x+2)=0

x^{2} (5 x - 7) (3 x + 2) = 0

x^3-3x^2-9x+21=0

x^{3} - 3 x^{2} - 9 x + 21 = 0

t^{3} = 30

x^4-2x^3+5x-1=0

x^{4} - 2 x^{3} + 5 x - 1 = 0

solvefor w,w^3=-2-2sqrt(3)i

so l v e f or w, w^{3} = - 2 - 23 i