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受欢迎的代数 >

(sqrt(6x+21)+3)^2=(x-2)^2

解答

(6 x + 21 + 3)^{2} = (x - 2)^{2}

解答

x = - 2.89897 \dots, x = 15.74596 \dots

求解步骤

(6 x + 21 + 3)^{2} = (x - 2)^{2}

用

6 x + 21 = u

和

x = \frac{u ^{2} - 21}{6}

改写方程式

(u + 3)^{2} = ((\frac{u ^{2} - 21}{6}) - 2)^{2}

解

(u + 3)^{2} = ((\frac{u ^{2} - 21}{6}) - 2)^{2} : u \approx 1.89897 \dots, u \approx - 4.74596 \dots, u \approx - 7.89897 \dots, u \approx 10.74596 \dots

u \approx 1.89897 \dots, u \approx - 4.74596 \dots, u \approx - 7.89897 \dots, u \approx 10.74596 \dots

代回

u = 6 x + 21

，求解

x

解

6 x + 21 = 1.89897 \dots : x = - 2.89897 \dots

解

6 x + 21 = - 4.74596 \dots : x \in R

无解

解

6 x + 21 = - 7.89897 \dots : x \in R

无解

解

6 x + 21 = 10.74596 \dots : x = 15.74596 \dots

x = - 2.89897 \dots, x = 15.74596 \dots

验证解:

x = - 2.89897 \dots

真

, x = 15.74596 \dots

真

解为

x = - 2.89897 \dots, x = 15.74596 \dots

作图

流行的例子

x + 3 = 9 - x

150*15=12sqrt(j)

150 \cdot 15 = 12 j

0 = x + 1 - 2

1/(sqrt(n))*100=5

\frac{1}{n} \cdot 100 = 5

sqrt(7x+126)=14

7 x + 126 = 14