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受欢迎的代数 >

x^3-3x^2+x-3=x^2+1

解答

x^{3} - 3 x^{2} + x - 3 = x^{2} + 1

解答

x = 4, x = i, x = - i

求解步骤

x^{3} - 3 x^{2} + x - 3 = x^{2} + 1

将

1

para o lado esquerdo

x^{3} - 3 x^{2} + x - 4 = x^{2}

将

x^{2}

para o lado esquerdo

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

因式分解

x^{3} - 4 x^{2} + x - 4 : (x - 4) (x^{2} + 1)

(x - 4) (x^{2} + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 4 = 0 or x^{2} + 1 = 0

解

x - 4 = 0 : x = 4

解

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

解为

x = 4, x = i, x = - i

作图

流行的例子

(x-2)^2(x+1)^2=0

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

solvefor y,y^3=x^2

so l v e f or y, y^{3} = x^{2}

x^{5} = 25 x^{3}

x^6+56x^3-512=0

x^{6} + 56 x^{3} - 512 = 0

2x^3-3x^2+8x-12=0

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