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受欢迎的代数 >

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

解答

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

解答

x = 3 - 22, x = 3 + 22

+1

十进制

x = 0.17157 \dots, x = 5.82842 \dots

求解步骤

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

展开

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

展开

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

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

将

2

para o lado esquerdo

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

将

4 x

para o lado esquerdo

x^{2} + 6 x - 1 = 2 x^{2}

将

2 x^{2}

para o lado esquerdo

- x^{2} + 6 x - 1 = 0

使用求根公式求解

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( - 1 ) ( - 1 )}{2 ( - 1 )}

6^{2} - 4 (- 1) (- 1) = 42

x_{1, 2} = \frac{- 6 \pm 4 2}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- 6 + 4 2}{2 ( - 1 )}, x_{2} = \frac{- 6 - 4 2}{2 ( - 1 )}

x = \frac{- 6 + 4 2}{2 ( - 1 )} : 3 - 22

x = \frac{- 6 - 4 2}{2 ( - 1 )} : 3 + 22

二次方程组的解是:

x = 3 - 22, x = 3 + 22

作图

流行的例子

x/3 =(5x-9)/4-(x-1)/2

\frac{x}{3} = \frac{5 x - 9}{4} - \frac{x - 1}{2}

因式分解 2k^2+k-10

f a c t or 2 k^{2} + k - 10

s im pl i f y 4^{- 6}

9 - 4 (2 p - 1) = 41

x^{2} + 8 x + 65 = 0