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受欢迎的代数 >

(x-4)(x^2+10x+52)=(x-4)^2

解答

(x - 4) (x^{2} + 10 x + 52) = (x - 4)^{2}

解答

x = 4, x = - \frac{9}{2} + i \frac{143}{2}, x = - \frac{9}{2} - i \frac{143}{2}

求解步骤

(x - 4) (x^{2} + 10 x + 52) = (x - 4)^{2}

展开

(x - 4) (x^{2} + 10 x + 52) : x^{3} + 6 x^{2} + 12 x - 208

展开

(x - 4)^{2} : x^{2} - 8 x + 16

x^{3} + 6 x^{2} + 12 x - 208 = x^{2} - 8 x + 16

将

16

para o lado esquerdo

x^{3} + 6 x^{2} + 12 x - 224 = x^{2} - 8 x

将

8 x

para o lado esquerdo

x^{3} + 6 x^{2} + 20 x - 224 = x^{2}

将

x^{2}

para o lado esquerdo

x^{3} + 5 x^{2} + 20 x - 224 = 0

因式分解

x^{3} + 5 x^{2} + 20 x - 224 : (x - 4) (x^{2} + 9 x + 56)

(x - 4) (x^{2} + 9 x + 56) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 4 = 0 or x^{2} + 9 x + 56 = 0

解

x - 4 = 0 : x = 4

解

x^{2} + 9 x + 56 = 0 : x = - \frac{9}{2} + i \frac{143}{2}, x = - \frac{9}{2} - i \frac{143}{2}

解为

x = 4, x = - \frac{9}{2} + i \frac{143}{2}, x = - \frac{9}{2} - i \frac{143}{2}

作图

流行的例子

8t^3-72t^2+228t-252=0

8 t^{3} - 72 t^{2} + 228 t - 252 = 0

-19.6x^3+26.067x^2-7.29=0

- 19.6 x^{3} + 26.067 x^{2} - 7.29 = 0

x^{3} = a

2x^3-4x^2-10x+12=0

2 x^{3} - 4 x^{2} - 10 x + 12 = 0

q^{(4)}-q^{(2)}-6=0

q^{(4)} - q^{(2)} - 6 = 0