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受欢迎的代数 >

x^3+x=x^2+1

解答

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

解答

x = 1, x = i, x = - i

求解步骤

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

将

1

para o lado esquerdo

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

将

x^{2}

para o lado esquerdo

x^{3} + x - 1 - x^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{3} - x^{2} + x - 1 = 0

因式分解

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

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

x - 1 = 0 : x = 1

解

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

解为

x = 1, x = i, x = - i

作图

流行的例子

2x^3+3x^2-36x+6=0

2 x^{3} + 3 x^{2} - 36 x + 6 = 0

x^3-2x^2-5x-6=0

x^{3} - 2 x^{2} - 5 x - 6 = 0

155 = 5 x^{3}

solvefor x,-3x^3+75x=0

so l v e f or x, - 3 x^{3} + 75 x = 0

128 = x^{7}