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受欢迎的代数 >

5x^5=-40x^2

解答

5 x^{5} = - 40 x^{2}

解答

x = 0, x = - 2, x = 1 + 3 i, x = 1 - 3 i

求解步骤

5 x^{5} = - 40 x^{2}

将

40 x^{2}

para o lado esquerdo

5 x^{5} + 40 x^{2} = 0

因式分解

5 x^{5} + 40 x^{2} : 5 x^{2} (x + 2) (x^{2} - 2 x + 4)

5 x^{2} (x + 2) (x^{2} - 2 x + 4) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or x + 2 = 0 or x^{2} - 2 x + 4 = 0

解

x + 2 = 0 : x = - 2

解

x^{2} - 2 x + 4 = 0 : x = 1 + 3 i, x = 1 - 3 i

解为

x = 0, x = - 2, x = 1 + 3 i, x = 1 - 3 i

作图

流行的例子

λ^3-3λ^2+3λ-1=0

λ^{3} - 3 λ^{2} + 3 λ - 1 = 0

5 - 1 x^{3} = - 15

x^3-3x^2-4x-12=0

x^{3} - 3 x^{2} - 4 x - 12 = 0

x^{4} + 2 x^{2} + 5 = 0

solvefor y,y^6=x

so l v e f or y, y^{6} = x