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受欢迎的代数 >

p^3+3p^2+2p=7980

解答

p^{3} + 3 p^{2} + 2 p = 7980

解答

p = 19, p = - 11 + 299 i, p = - 11 - 299 i

求解步骤

p^{3} + 3 p^{2} + 2 p = 7980

将

7980

para o lado esquerdo

p^{3} + 3 p^{2} + 2 p - 7980 = 0

因式分解

p^{3} + 3 p^{2} + 2 p - 7980 : (p - 19) (p^{2} + 22 p + 420)

(p - 19) (p^{2} + 22 p + 420) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

p - 19 = 0 or p^{2} + 22 p + 420 = 0

解

p - 19 = 0 : p = 19

解

p^{2} + 22 p + 420 = 0 : p = - 11 + 299 i, p = - 11 - 299 i

解为

p = 19, p = - 11 + 299 i, p = - 11 - 299 i

作图

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