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受欢迎的代数 >

r^3-7r^2-7r-8=0

解答

r^{3} - 7 r^{2} - 7 r - 8 = 0

解答

r = 8, r = - \frac{1}{2} + i \frac{3}{2}, r = - \frac{1}{2} - i \frac{3}{2}

求解步骤

r^{3} - 7 r^{2} - 7 r - 8 = 0

因式分解

r^{3} - 7 r^{2} - 7 r - 8 : (r - 8) (r^{2} + r + 1)

(r - 8) (r^{2} + r + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

r - 8 = 0 or r^{2} + r + 1 = 0

解

r - 8 = 0 : r = 8

解

r^{2} + r + 1 = 0 : r = - \frac{1}{2} + i \frac{3}{2}, r = - \frac{1}{2} - i \frac{3}{2}

解为

r = 8, r = - \frac{1}{2} + i \frac{3}{2}, r = - \frac{1}{2} - i \frac{3}{2}

作图

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