Question

Bài 33 (trang 19 SGK Toán 9 Tập 1)

Giải phương trình

a) $\sqrt{2}.x-\sqrt{50}=0$ ;                                           b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$ ;

c) $\sqrt{3}.x^2-\sqrt{12}=0$ ;                                         d) $\dfrac{x^2}{\sqrt{5}}-\sqrt{20}=0$.

Answer 1

a)

b)

c)

 

d)

#Học tốt!!!

Answer 2

 a)

b)

c)

d)

 

Answer 3

a, \(\sqrt{2}x-\sqrt{50}=0\Leftrightarrow\sqrt{2}x-5\sqrt{2}=0\)

\(\Leftrightarrow\sqrt{2}\left(x-5\right)=0\Leftrightarrow x=5\)

Vậy tập nghiệm của phương trình là S = { 5 } 

b, \(\sqrt{3}x+\sqrt{3}=\sqrt{12}+\sqrt{27}\)

\(\Leftrightarrow x\sqrt{3}+\sqrt{3}-2\sqrt{3}-3\sqrt{3}=0\)

\(\Leftrightarrow\sqrt{3}\left(x+1-2-3\right)=0\Leftrightarrow\sqrt{3}\left(x-4\right)=0\Leftrightarrow x=4\)

Vậy tập nghiệm của phương trình là S = { 4 } 

c, \(x^2\sqrt{3}-\sqrt{12}=0\Leftrightarrow x^2\sqrt{3}-2\sqrt{3}=0\)

\(\Leftrightarrow\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)=0\Leftrightarrow x=\pm\sqrt{2}\)

Vậy tập nghiệm của phương trình là S = { \(\pm\sqrt{2}\)}

d, \(\frac{x^2}{\sqrt{5}}-\sqrt{20}=0\Leftrightarrow\frac{x^2}{\sqrt{5}}-2\sqrt{5}=0\)

\(\Leftrightarrow\frac{x^2}{\sqrt{5}}-\frac{10}{\sqrt{5}}=0\Leftrightarrow\left(x-\sqrt{10}\right)\left(x+\sqrt{10}\right)=0\Leftrightarrow x=\pm\sqrt{10}\)

Vậy tập nghiệm của phương trình là S = { \(\pm\sqrt{10}\)}

Answer 4

a) x = 5

b) x= 4 

c) x = +_ căn 2

d ) x= +_ căn 10 

Answer 5

a) $\sqrt{2}.x-\sqrt{50}=0$

$\iff$ $\sqrt{2}x=\sqrt{50}$

502

502

$\iff$ $x=\sqrt{25}$

$\iff$ $x=5$.

Vậy $x=5$.

b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$

$\iff$ $\sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=4\sqrt{3}$

433

$\iff$ $x=4$.

Vậy $x=4$.

c) $\sqrt{3}.x^2-\sqrt{12}=0$
$\iff$ $\sqrt{3}{x}^2=\sqrt{12}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4.3}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4}.\sqrt{3}$
$\iff$ $x^2=\sqrt{4}$
$\iff$ $x^2=\sqrt{2^2}$
$\iff$ $x^2=2$
$\iff$ $\sqrt{x^2}=\sqrt{2}$
$\iff$ $|x|=\sqrt{2}$
$\iff$ $x=\pm \sqrt{2}$.

Vậy $x=\pm \sqrt{2}$.

x25−20=0

$\iff$ $x^2=\sqrt{20}.\sqrt{5}$
$\iff$ $x^2=\sqrt{20.5}$
$\iff$ $x^2=\sqrt{100}$
$\iff$ $x^2=\sqrt{{10}^2}$
$\iff$ $x^2=10$
$\iff$ $\sqrt{x^2}=\sqrt{10}$
$\iff$ $|x|=\sqrt{10}$
$\iff$ $x=\pm \sqrt{10}$
Vậy $x=\pm \sqrt{10}$.

Answer 6

a) $\sqrt{2}.x-\sqrt{50}=0$

$\iff$ $\sqrt{2}x=\sqrt{50}$

502

502

$\iff$ $x=\sqrt{25}$

$\iff$ $x=5$.

Vậy $x=5$.

b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$

$\iff$ $\sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=4\sqrt{3}$

433

$\iff$ $x=4$.

Vậy $x=4$.

c) $\sqrt{3}.x^2-\sqrt{12}=0$
$\iff$ $\sqrt{3}{x}^2=\sqrt{12}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4.3}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4}.\sqrt{3}$
$\iff$ $x^2=\sqrt{4}$
$\iff$ $x^2=\sqrt{2^2}$
$\iff$ $x^2=2$
$\iff$ $\sqrt{x^2}=\sqrt{2}$
$\iff$ $|x|=\sqrt{2}$
$\iff$ $x=\pm \sqrt{2}$.

Vậy $x=\pm \sqrt{2}$.

x25−20=0

$\iff$ $x^2=\sqrt{20}.\sqrt{5}$
$\iff$ $x^2=\sqrt{20.5}$
$\iff$ $x^2=\sqrt{100}$
$\iff$ $x^2=\sqrt{{10}^2}$
$\iff$ $x^2=10$
$\iff$ $\sqrt{x^2}=\sqrt{10}$
$\iff$ $|x|=\sqrt{10}$
$\iff$ $x=\pm \sqrt{10}$
Vậy $x=\pm \sqrt{10}$.

Answer 7

) $\sqrt{2}.x-\sqrt{50}=0$

$\iff$ $\sqrt{2}x=\sqrt{50}$

502

502

$\iff$ $x=\sqrt{25}$

$\iff$ $x=5$.

Vậy $x=5$.

b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$

$\iff$ $\sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=4\sqrt{3}$

433

$\iff$ $x=4$.

Vậy $x=4$.

c) $\sqrt{3}.x^2-\sqrt{12}=0$
$\iff$ $\sqrt{3}{x}^2=\sqrt{12}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4.3}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4}.\sqrt{3}$
$\iff$ $x^2=\sqrt{4}$
$\iff$ $x^2=\sqrt{2^2}$
$\iff$ $x^2=2$
$\iff$ $\sqrt{x^2}=\sqrt{2}$
$\iff$ $|x|=\sqrt{2}$
$\iff$ $x=\pm \sqrt{2}$.

Vậy $x=\pm \sqrt{2}$.

x25−20=0

$\iff$ $x^2=\sqrt{20}.\sqrt{5}$
$\iff$ $x^2=\sqrt{20.5}$
$\iff$ $x^2=\sqrt{100}$
$\iff$ $x^2=\sqrt{{10}^2}$
$\iff$ $x^2=10$
$\iff$ $\sqrt{x^2}=\sqrt{10}$
$\iff$ $|x|=\sqrt{10}$
$\iff$ $x=\pm \sqrt{10}$
Vậy $x=\pm \sqrt{10}$.

Answer 8

Answer 9

a) \(\sqrt{2}x-\sqrt{50}=0\Leftrightarrow\sqrt{2}x=\sqrt{50}\Rightarrow x=\sqrt{25}=5\)

b) \(\sqrt{3}x+\sqrt{3}=\sqrt{12}+\sqrt{27}\Leftrightarrow\sqrt{3}.\left(x+1\right)=\sqrt{3}.\left(\sqrt{4}+\sqrt{9}\right)\Leftrightarrow\sqrt{3}.\left(x+1-2-3\right)=0\Leftrightarrow\sqrt{3}.(x-4)=0\Rightarrow x-4=0\Leftrightarrow x=4\)

c) \(\sqrt{3}x^2-\sqrt{12}=0\Leftrightarrow\sqrt{3}.\left(x^2-\sqrt{4}\right)=0\Rightarrow x^2=2\Rightarrow x\in\left\{\pm\sqrt{2}\right\}\)

d) \(\dfrac{x^2}{\sqrt{5}}-\sqrt{20}=0\Leftrightarrow\dfrac{x^2-\sqrt{100}}{\sqrt{5}}=0\Rightarrow x^2=\sqrt{100}=10\Rightarrow x\in\left\{\pm\sqrt{10}\right\}\)

Answer 10

\(a=5;x=4;x=+-\sqrt{2};+-\sqrt{10}\)

Answer 11

a) \sqrt{2}.x-\sqrt{50}=02​.x−50​=0

$\iff$ \sqrt{2}x=\sqrt{50}2​x=50​

$\iff$ x=\dfrac{\sqrt{50}}{\sqrt{2}}x=2​50​​

$\iff$ x=\sqrt{\dfrac{50}{2}}x=250​​

$\iff$ x=\sqrt{25}x=25​

$\iff$ $x=5$.

Vậy $x=5$.

b) \sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}3​.x+3​=12​+27​

$\iff$ \sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}3​x=12​+27​−3​

$\iff$ \sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}3​x=4.3​+9.3​−3​

$\iff$ \sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}3​x=4​.3​+9​.3​−3​

$\iff$ \sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}3​x=23​+33​−3​

$\iff$ \sqrt{3}x=4\sqrt{3}3​x=43​

$\iff$ x=\dfrac{4\sqrt{3}}{\sqrt{3}}x=3​43​​

$\iff$ $x=4$.

Vậy $x=4$.

c) \sqrt{3}.x^2-\sqrt{12}=03​.x2−12​=0
$\iff$ \sqrt{3} x^{2}=\sqrt{12}3​x2=12​
$\iff$ \sqrt{3} x^{2}=\sqrt{4.3}3​x2=4.3​
$\iff$ \sqrt{3} x^{2}=\sqrt{4}.\sqrt{3}3​x2=4​.3​
$\iff$ x^{2}=\sqrt{4}x2=4​
$\iff$ x^{2}=\sqrt{2^{2}}x2=22​
$\iff$ x^{2}=2x2=2
$\iff$ \sqrt{x^{2}}=\sqrt{2}x2​=2​
$\iff$ |x|=\sqrt{2}∣x∣=2​
$\iff$ x=\pm \sqrt{2}x=±2​.

Vậy x=\pm \sqrt{2}x=±2​.

d) \dfrac{x^2}{\sqrt{5}}-\sqrt{20}=05​x2​−20​=0
$\iff$ \dfrac{x^{2}}{\sqrt{5}}=\sqrt{20}5​x2​=20​
$\iff$ x^{2}=\sqrt{20}.\sqrt{5}x2=20​.5​
$\iff$ x^{2}=\sqrt{20.5}x2=20.5​
$\iff$ x^{2}=\sqrt{100}x2=100​
$\iff$ x^{2}=\sqrt{10^{2}}x2=102​
$\iff$ x^{2}=10x2=10
$\iff$ \sqrt{x^{2}}=\sqrt{10}x2​=10​
$\iff$ |x|=\sqrt{10}∣x∣=10​
$\iff$ x=\pm \sqrt{10}x=±10​
Vậy x=\pm \sqrt{10}x=±10​.

Answer 12

a) $\sqrt{2}.x-\sqrt{50}=0$

$\iff$ $\sqrt{2}x=\sqrt{50}$

502

502

$\iff$ $x=\sqrt{25}$

$\iff$ $x=5$.

Vậy $x=5$.

b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$

$\iff$ $\sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=4\sqrt{3}$

433

$\iff$ $x=4$.

Vậy $x=4$.

c) $\sqrt{3}.x^2-\sqrt{12}=0$
$\iff$ $\sqrt{3}{x}^2=\sqrt{12}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4.3}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4}.\sqrt{3}$
$\iff$ $x^2=\sqrt{4}$
$\iff$ $x^2=\sqrt{2^2}$
$\iff$ $x^2=2$
$\iff$ $\sqrt{x^2}=\sqrt{2}$
$\iff$ $|x|=\sqrt{2}$
$\iff$ $x=\pm \sqrt{2}$.

Vậy $x=\pm \sqrt{2}$.

x25−20=0

$\iff$ $x^2=\sqrt{20}.\sqrt{5}$
$\iff$ $x^2=\sqrt{20.5}$
$\iff$ $x^2=\sqrt{100}$
$\iff$ $x^2=\sqrt{{10}^2}$
$\iff$ $x^2=10$
$\iff$ $\sqrt{x^2}=\sqrt{10}$
$\iff$ $|x|=\sqrt{10}$
$\iff$ $x=\pm \sqrt{10}$
Vậy $x=\pm \sqrt{10}$.
 

Answer 13

a) $\sqrt{2}.x-\sqrt{50}=0$

$\iff$ $\sqrt{2}x=\sqrt{50}$

502

502

$\iff$ $x=\sqrt{25}$

$\iff$ $x=5$.

Vậy $x=5$.

b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$

$\iff$ $\sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=4\sqrt{3}$

433

$\iff$ $x=4$.

Vậy $x=4$.

c) $\sqrt{3}.x^2-\sqrt{12}=0$
$\iff$ $\sqrt{3}{x}^2=\sqrt{12}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4.3}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4}.\sqrt{3}$
$\iff$ $x^2=\sqrt{4}$
$\iff$ $x^2=\sqrt{2^2}$
$\iff$ $x^2=2$
$\iff$ $\sqrt{x^2}=\sqrt{2}$
$\iff$ $|x|=\sqrt{2}$
$\iff$ $x=\pm \sqrt{2}$.

Vậy $x=\pm \sqrt{2}$.

x25−20=0

$\iff$ $x^2=\sqrt{20}.\sqrt{5}$
$\iff$ $x^2=\sqrt{20.5}$
$\iff$ $x^2=\sqrt{100}$
$\iff$ $x^2=\sqrt{{10}^2}$
$\iff$ $x^2=10$
$\iff$ $\sqrt{x^2}=\sqrt{10}$
$\iff$ $|x|=\sqrt{10}$
$\iff$ $x=\pm \sqrt{10}$
Vậy $x=\pm \sqrt{10}$.
 

Answer 14

a) x=5

b) x=4

c) x=\(+-\sqrt{2}\)

d) x=+- sqrt(10)

Answer 15

a, \(\sqrt{2}.x-\sqrt{50}=0\)
<=> \(\sqrt{2}.x=\sqrt{50} \)
<=> \(\sqrt{2}.x=\sqrt{25.2}\)
<=>\(x=\sqrt{25}\)
<=>x=5

Answer 16

a) \sqrt{2}.x-\sqrt{50}=02​.x−50​=0

$\iff$ \sqrt{2}x=\sqrt{50}2​x=50​

$\iff$ x=\dfrac{\sqrt{50}}{\sqrt{2}}x=2​50​​

$\iff$ x=\sqrt{\dfrac{50}{2}}x=250​​

$\iff$ x=\sqrt{25}x=25​

$\iff$ $x=5$.

Vậy $x=5$.

b) \sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}3​.x+3​=12​+27​

$\iff$ \sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}3​x=12​+27​−3​

$\iff$ \sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}3​x=4.3​+9.3​−3​

$\iff$ \sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}3​x=4​.3​+9​.3​−3​

$\iff$ \sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}3​x=23​+33​−3​

$\iff$ \sqrt{3}x=4\sqrt{3}3​x=43​

$\iff$ x=\dfrac{4\sqrt{3}}{\sqrt{3}}x=3​43​​

$\iff$ $x=4$.

Vậy $x=4$.

c) \sqrt{3}.x^2-\sqrt{12}=03​.x2−12​=0
$\iff$ \sqrt{3} x^{2}=\sqrt{12}3​x2=12​
$\iff$ \sqrt{3} x^{2}=\sqrt{4.3}3​x2=4.3​
$\iff$ \sqrt{3} x^{2}=\sqrt{4}.\sqrt{3}3​x2=4​.3​
$\iff$ x^{2}=\sqrt{4}x2=4​
$\iff$ x^{2}=\sqrt{2^{2}}x2=22​
$\iff$ x^{2}=2x2=2
$\iff$ \sqrt{x^{2}}=\sqrt{2}x2​=2​
$\iff$ |x|=\sqrt{2}∣x∣=2​
$\iff$ x=\pm \sqrt{2}x=±2​.

Vậy x=\pm \sqrt{2}x=±2​.

d) \dfrac{x^2}{\sqrt{5}}-\sqrt{20}=05​x2​−20​=0
$\iff$ \dfrac{x^{2}}{\sqrt{5}}=\sqrt{20}5​x2​=20​
$\iff$ x^{2}=\sqrt{20}.\sqrt{5}x2=20​.5​
$\iff$ x^{2}=\sqrt{20.5}x2=20.5​
$\iff$ x^{2}=\sqrt{100}x2=100​
$\iff$ x^{2}=\sqrt{10^{2}}x2=102​
$\iff$ x^{2}=10x2=10
$\iff$ \sqrt{x^{2}}=\sqrt{10}x2​=10​
$\iff$ |x|=\sqrt{10}∣x∣=10​
$\iff$ x=\pm \sqrt{10}x=±10​
Vậy x=\pm \sqrt{10}x=±10​.

Answer 17

a, ⇔\(\sqrt{2}\).x =\(\sqrt{50}\)

⇔\(\sqrt{2}\).x = \(\sqrt{25.2}\)⇒\(\sqrt{2}\).x=\(\sqrt{2}\).\(\sqrt{25}\)⇒x =\(\sqrt{25}\) = 5 

b, ⇔\(\sqrt{3}\). ( x+1) = \(\sqrt{4.3}\) +\(\sqrt{9}.3\)⇒\(\sqrt{3}\).(x+1) ⇒ \(\sqrt{4}\). \(\sqrt{3}\)+ \(\sqrt{9}\) .\(\sqrt{3}\) ⇒ \(\sqrt{3}\).(x+) =\(\sqrt{3}\). ( \(\sqrt{4}\)+\(\sqrt{9}\)) 

⇒x + 1 = 2 +3 ⇔ x+1 = 5 ⇔ x = 5-1 =4  Vậy x = 4 

c, ⇔ \(\sqrt{3}\)x² =\(\sqrt{12}\) ⇒ \(\sqrt{3}\)x² = \(\sqrt{4.3}\) ⇒\(\sqrt{3}\). x² =\(\sqrt{4}\).\(\sqrt{3}\) ⇒ \(\sqrt{3}\). x² = 2 .\(\sqrt{3}\) 

 ⇔ x² =2 ⇒\(\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\)   Vậy x= \(\sqrt{2}\)  và x = -\(\sqrt{2}\)

Answer 18

a) $\sqrt{2}.x-\sqrt{50}=0$

$\iff$ $\sqrt{2}x=\sqrt{50}$

$\iff$ $x=\frac{\sqrt{50}}{\sqrt{2}}$

$\iff$ $x=\sqrt{\frac{50}{2}}$

$\iff$ $x=\sqrt{25}$

$\iff$ $x=5$.

Vậy $x=5$.

b) $\sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}$

$\iff$ $\sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}$

$\iff$ $\sqrt{3}x=4\sqrt{3}$

$\iff$ $x=\frac{4\sqrt{3}}{\sqrt{3}}$

$\iff$ $x=4$.

Vậy $x=4$.

c) $\sqrt{3}.x^2-\sqrt{12}=0$
$\iff$ $\sqrt{3}{x}^2=\sqrt{12}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4.3}$
$\iff$ $\sqrt{3}{x}^2=\sqrt{4}.\sqrt{3}$
$\iff$ $x^2=\sqrt{4}$
$\iff$ $x^2=\sqrt{2^2}$
$\iff$ $x^2=2$
$\iff$ $\sqrt{x^2}=\sqrt{2}$
$\iff$ $|x|=\sqrt{2}$
$\iff$ $x=\pm \sqrt{2}$.

Vậy $x=\pm \sqrt{2}$.

d) $\frac{x^2}{\sqrt{5}}-\sqrt{20}=0$
$\iff$ $\frac{x^2}{\sqrt{5}}=\sqrt{20}$
$\iff$ $x^2=\sqrt{20}.\sqrt{5}$
$\iff$ $x^2=\sqrt{20.5}$
$\iff$ $x^2=\sqrt{100}$
$\iff$ $x^2=\sqrt{{10}^2}$
$\iff$ $x^2=10$
$\iff$ $\sqrt{x^2}=\sqrt{10}$
$\iff$ $|x|=\sqrt{10}$
$\iff$ $x=\pm \sqrt{10}$
Vậy $x=\pm \sqrt{10}$.

Answer 19

Answer 20

Answer 21

a) \sqrt{2}.x-\sqrt{50}=02​.x−50​=0

$\iff$ \sqrt{2}x=\sqrt{50}2​x=50​

$\iff$ x=\dfrac{\sqrt{50}}{\sqrt{2}}x=2​50​​

$\iff$ x=\sqrt{\dfrac{50}{2}}x=250​​

$\iff$ x=\sqrt{25}x=25​

$\iff$ $x=5$.

Vậy $x=5$.

b) \sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}3​.x+3​=12​+27​

$\iff$ \sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}3​x=12​+27​−3​

$\iff$ \sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}3​x=4.3​+9.3​−3​

$\iff$ \sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}3​x=4​.3​+9​.3​−3​

$\iff$ \sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}3​x=23​+33​−3​

$\iff$ \sqrt{3}x=4\sqrt{3}3​x=43​

$\iff$ x=\dfrac{4\sqrt{3}}{\sqrt{3}}x=3​43​​

$\iff$ $x=4$.

Vậy $x=4$.

c) \sqrt{3}.x^2-\sqrt{12}=03​.x2−12​=0
$\iff$ \sqrt{3} x^{2}=\sqrt{12}3​x2=12​
$\iff$ \sqrt{3} x^{2}=\sqrt{4.3}3​x2=4.3​
$\iff$ \sqrt{3} x^{2}=\sqrt{4}.\sqrt{3}3​x2=4​.3​
$\iff$ x^{2}=\sqrt{4}x2=4​
$\iff$ x^{2}=\sqrt{2^{2}}x2=22​
$\iff$ x^{2}=2x2=2
$\iff$ \sqrt{x^{2}}=\sqrt{2}x2​=2​
$\iff$ |x|=\sqrt{2}∣x∣=2​
$\iff$ x=\pm \sqrt{2}x=±2​.

Vậy x=\pm \sqrt{2}x=±2​.

d) \dfrac{x^2}{\sqrt{5}}-\sqrt{20}=05​x2​−20​=0
$\iff$ \dfrac{x^{2}}{\sqrt{5}}=\sqrt{20}5​x2​=20​
$\iff$ x^{2}=\sqrt{20}.\sqrt{5}x2=20​.5​
$\iff$ x^{2}=\sqrt{20.5}x2=20.5​
$\iff$ x^{2}=\sqrt{100}x2=100​
$\iff$ x^{2}=\sqrt{10^{2}}x2=102​
$\iff$ x^{2}=10x2=10
$\iff$ \sqrt{x^{2}}=\sqrt{10}x2​=10​
$\iff$ |x|=\sqrt{10}∣x∣=10​
$\iff$ x=\pm \sqrt{10}x=±10​
Vậy x=\pm \sqrt{10}x=±10​.

Answer 22

Answer 23

Answer 24

.

Answer 25

a) x=5

b x=4

c) x=+- căn 2

d) x=+- căn 10

Answer 26

a) √2.x−√50=0

⇔ √2x=√50

⇔ x=√50√2

⇔ x=√502

⇔ x=√25

⇔ x=5.

Vậy x=5.

b) √3.x+√3=√12+√27

⇔ √3x=√12+√27−√3

⇔ √3x=√4.3+√9.3−√3

⇔ √3x=√4.√3+√9.√3−√3

⇔ √3x=2√3+3√3−√3

⇔ √3x=4√3

⇔ x=4√3√3

⇔ x=4.

Vậy x=4.

2−√12=0
2=√12
2=√4.3
2=√4.√3
2=√4
2
2=2
2=√2
⇔ |x|=√2
⇔ x=±√2.

Vậy x=±√2.

2√5−√20=0
2√5=√20
2=√20.√5
2=√20.5
2=√100
2
2=10
2=√10
⇔ |x|=√10
⇔ x=±√10
Vậy x=±√10.

Answer 27

a)

b)

c)

d)

 

Answer 28

a,5

b,4

c,x=-2    x=2

d,

Answer 29

a) \sqrt{2}.x-\sqrt{50}=02​.x−50​=0

$\iff$ \sqrt{2}x=\sqrt{50}2​x=50​

$\iff$ x=\dfrac{\sqrt{50}}{\sqrt{2}}x=2​50​​

$\iff$ x=\sqrt{\dfrac{50}{2}}x=250​​

$\iff$ x=\sqrt{25}x=25​

$\iff$ $x=5$.

Vậy $x=5$.

b) \sqrt{3}.x+\sqrt{3}=\sqrt{12}+\sqrt{27}3​.x+3​=12​+27​

$\iff$ \sqrt{3}x=\sqrt{12}+\sqrt{27}-\sqrt{3}3​x=12​+27​−3​

$\iff$ \sqrt{3}x=\sqrt{4.3}+\sqrt{9.3}-\sqrt{3}3​x=4.3​+9.3​−3​

$\iff$ \sqrt{3}x=\sqrt{4}.\sqrt{3}+\sqrt{9}.\sqrt{3}-\sqrt{3}3​x=4​.3​+9​.3​−3​

$\iff$ \sqrt{3}x=2\sqrt{3}+3\sqrt{3}-\sqrt{3}3​x=23​+33​−3​

$\iff$ \sqrt{3}x=4\sqrt{3}3​x=43​

$\iff$ x=\dfrac{4\sqrt{3}}{\sqrt{3}}x=3​43​​

$\iff$ $x=4$.

Vậy $x=4$.

c) \sqrt{3}.x^2-\sqrt{12}=03​.x2−12​=0
$\iff$ \sqrt{3} x^{2}=\sqrt{12}3​x2=12​
$\iff$ \sqrt{3} x^{2}=\sqrt{4.3}3​x2=4.3​
$\iff$ \sqrt{3} x^{2}=\sqrt{4}.\sqrt{3}3​x2=4​.3​
$\iff$ x^{2}=\sqrt{4}x2=4​
$\iff$ x^{2}=\sqrt{2^{2}}x2=22​
$\iff$ x^{2}=2x2=2
$\iff$ \sqrt{x^{2}}=\sqrt{2}x2​=2​
$\iff$ |x|=\sqrt{2}∣x∣=2​
$\iff$ x=\pm \sqrt{2}x=±2​.

Vậy x=\pm \sqrt{2}x=±2​.

d) \dfrac{x^2}{\sqrt{5}}-\sqrt{20}=05​x2​−20​=0
$\iff$ \dfrac{x^{2}}{\sqrt{5}}=\sqrt{20}5​x2​=20​
$\iff$ x^{2}=\sqrt{20}.\sqrt{5}x2=20​.5​
$\iff$ x^{2}=\sqrt{20.5}x2=20.5​
$\iff$ x^{2}=\sqrt{100}x2=100​
$\iff$ x^{2}=\sqrt{10^{2}}x2=102​
$\iff$ x^{2}=10x2=10
$\iff$ \sqrt{x^{2}}=\sqrt{10}x2​=10​
$\iff$ |x|=\sqrt{10}∣x∣=10​
$\iff$ x=\pm \sqrt{10}x=±10​
Vậy x=\pm \sqrt{10}x=±10​.

Answer 30

a)\(x=5\)

b)\(x=4\)

c)\(x=\pm\sqrt{2}\)

d)\(x=\pm\sqrt{10}\)