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受欢迎的代数 >

(3x^2-4x-5)^2=-3x^2+4x+5

解答

(3 x^{2} - 4 x - 5)^{2} = - 3 x^{2} + 4 x + 5

解答

x = 2, x = - \frac{2}{3}, x = \frac{2 + 19}{3}, x = \frac{2 - 19}{3}

+1

十进制

x = 2, x = - 0.66666 \dots, x = 2.11963 \dots, x = - 0.78629 \dots

求解步骤

(3 x^{2} - 4 x - 5)^{2} = - 3 x^{2} + 4 x + 5

展开

(3 x^{2} - 4 x - 5)^{2} : 9 x^{4} - 24 x^{3} - 14 x^{2} + 40 x + 25

9 x^{4} - 24 x^{3} - 14 x^{2} + 40 x + 25 = - 3 x^{2} + 4 x + 5

将

5

para o lado esquerdo

9 x^{4} - 24 x^{3} - 14 x^{2} + 40 x + 20 = - 3 x^{2} + 4 x

将

4 x

para o lado esquerdo

9 x^{4} - 24 x^{3} - 14 x^{2} + 36 x + 20 = - 3 x^{2}

将

3 x^{2}

para o lado esquerdo

9 x^{4} - 24 x^{3} - 11 x^{2} + 36 x + 20 = 0

因式分解

9 x^{4} - 24 x^{3} - 11 x^{2} + 36 x + 20 : (x - 2) (3 x + 2) (3 x^{2} - 4 x - 5)

(x - 2) (3 x + 2) (3 x^{2} - 4 x - 5) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 2 = 0 or 3 x + 2 = 0 or 3 x^{2} - 4 x - 5 = 0

解

x - 2 = 0 : x = 2

解

3 x + 2 = 0 : x = - \frac{2}{3}

解

3 x^{2} - 4 x - 5 = 0 : x = \frac{2 + 19}{3}, x = \frac{2 - 19}{3}

解为

x = 2, x = - \frac{2}{3}, x = \frac{2 + 19}{3}, x = \frac{2 - 19}{3}

作图

流行的例子

(1 + x)^{4} = 1.4

-λ^3+2λ^2+5λ-6=0

- λ^{3} + 2 λ^{2} + 5 λ - 6 = 0

2c^3+4c^2-126c=0

2 c^{3} + 4 c^{2} - 126 c = 0

-x^3+11x^2-43x+25=0

- x^{3} + 11 x^{2} - 43 x + 25 = 0

q^{3} - q = 34 + 32 q