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受欢迎的代数 >

f=f^5

解答

f = f^{5}

解答

f = 0, f = i, f = - i, f = - 1, f = 1

求解步骤

f = f^{5}

交换两边

f^{5} = f

将

f

para o lado esquerdo

f^{5} - f = 0

因式分解

f^{5} - f : f (f^{2} + 1) (f + 1) (f - 1)

f (f^{2} + 1) (f + 1) (f - 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

f = 0 or f^{2} + 1 = 0 or f + 1 = 0 or f - 1 = 0

解

f^{2} + 1 = 0 : f = i, f = - i

解

f + 1 = 0 : f = - 1

解

f - 1 = 0 : f = 1

解为

f = 0, f = i, f = - i, f = - 1, f = 1

作图

流行的例子

d^{3} = 729

3 x^{3} - 2 a^{2} x = 0

solvefor z,z^5-32i=0

so l v e f or z, z^{5} - 32 i = 0

2(2x-5)-x^2+17x=16x^4

2 (2 x - 5) - x^{2} + 17 x = 16 x^{4}

2 x^{3} - 9 x^{2} + 10 = 0