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受欢迎的代数 >

(x^2+2x)^2=2x^2+4x+3

解答

(x^{2} + 2 x)^{2} = 2 x^{2} + 4 x + 3

解答

x = - 1, x = - 3, x = 1

求解步骤

(x^{2} + 2 x)^{2} = 2 x^{2} + 4 x + 3

展开

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

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

将

3

para o lado esquerdo

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

将

4 x

para o lado esquerdo

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

将

2 x^{2}

para o lado esquerdo

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

因式分解

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

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

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 1 = 0 or x + 3 = 0 or x - 1 = 0

解

x + 1 = 0 : x = - 1

解

x + 3 = 0 : x = - 3

解

x - 1 = 0 : x = 1

解为

x = - 1, x = - 3, x = 1

作图

流行的例子

p^{3} - 144 p = 0

x^{3} - 9 x^{2} - 22 x = 0

x^{3} + 2 x^{2} - 7 x = - 4

(x+2i)(x-2i)(x-5)=0

(x + 2 i) (x - 2 i) (x - 5) = 0

5x^3+13x^2-56x+20=0

5 x^{3} + 13 x^{2} - 56 x + 20 = 0