zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

(6x^2)/((sqrt(2x+1)+1)^2)=2x+sqrt(x-1)+1

解答

\frac{6 x ^{2}}{( 2 x + 1 + 1 ) ^{2}} = 2 x + x - 1 + 1

解答

x = 23.56067 \dots

求解步骤

\frac{6 x ^{2}}{( 2 x + 1 + 1 ) ^{2}} = 2 x + x - 1 + 1

在两边乘以

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

\frac{6 x ^{2}}{( 2 x + 1 + 1 ) ^{2}} (2 x + 1 + 1)^{2} = 2 x (2 x + 1 + 1)^{2} + x - 1 (2 x + 1 + 1)^{2} + 1 \cdot (2 x + 1 + 1)^{2}

化简

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

展开

2 x (2 x + 1 + 1)^{2} + x - 1 (2 x + 1 + 1)^{2} + (2 x + 1 + 1)^{2} : 4 x^{2} + 6 x + 4 x 2 x + 1 + 2 x x - 1 + 2 x - 1 + 2 x - 1 2 x + 1 + 2 2 x + 1 + 2

6 x^{2} = 4 x^{2} + 6 x + 4 x 2 x + 1 + 2 x x - 1 + 2 x - 1 + 2 x - 1 2 x + 1 + 2 2 x + 1 + 2

用

x - 1 = u

和

x = u^{2} + 1

改写方程式

6 (u^{2} + 1)^{2} = 4 (u^{2} + 1)^{2} + 6 (u^{2} + 1) + 4 (u^{2} + 1) 2 (u^{2} + 1) + 1 + 2 (u^{2} + 1) u + 2 u + 2 u 2 (u^{2} + 1) + 1 + 2 2 (u^{2} + 1) + 1 + 2

解

6 (u^{2} + 1)^{2} = 4 (u^{2} + 1)^{2} + 6 (u^{2} + 1) + 4 (u^{2} + 1) 2 (u^{2} + 1) + 1 + 2 (u^{2} + 1) u + 2 u + 2 u 2 (u^{2} + 1) + 1 + 2 2 (u^{2} + 1) + 1 + 2 : u \approx - 2.52756 \dots, u \approx 4.74980 \dots

u \approx - 2.52756 \dots, u \approx 4.74980 \dots

代回

u = x - 1

，求解

x

解

x - 1 = - 2.52756 \dots : x \in R

无解

解

x - 1 = 4.74980 \dots : x = 23.56067 \dots

x = 23.56067 \dots

验证解:

x = 23.56067 \dots

真

解是

x = 23.56067 \dots

作图

流行的例子

c= 1/((sqrt(x^2+x-2)))

c = \frac{1}{( x ^{2} + x - 2 )}

2x^2+2sqrt(5x)-5=0

2 x^{2} + 2 5 x - 5 = 0

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

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

sqrt(x+1)+sqrt(2x+3)=5

x + 1 + 2 x + 3 = 5

2 x - 3 = - 1