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AH
Akai Haruma
Giáo viên
23 tháng 10 2020

Lời giải:

a) ĐK: $x\geq 2$

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

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

\(\Rightarrow \left[\begin{matrix} \sqrt{x-2}=0\\ \sqrt{x+2}-3=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=2\\ x=7\end{matrix}\right.\) (thỏa mãn)

Vậy..........

b) ĐK: $x\geq 0$

PT $\Leftrightarrow (\sqrt{x}-3)^2=0$

$\Leftrightarrow \sqrt{x}-3=0$

$\Leftrightarrow x=9$ (thỏa mãn)

c) ĐK: $x\geq 3$

PT $\Leftrightarrow \sqrt{9(x-3)}+\sqrt{x-3}-\frac{1}{2}\sqrt{4(x-3)}=7$

$\Leftrightarrow 3\sqrt{x-3}+\sqrt{x-3}-\sqrt{x-3}=7$

$\Leftrightarrow 3\sqrt{x-3}=7$

$\Leftrightarrow x-3=(\frac{7}{3})^2$

$\Rightarrow x=\frac{76}{9}$

d)

ĐK: $x\geq \frac{-1}{2}$

PT $\Leftrightarrow 3\sqrt{4(2x+1)}-\frac{1}{3}\sqrt{9(2x+1)}-\frac{1}{2}\sqrt{25(2x+1)}+\sqrt{\frac{1}{4}(2x+1)}=6$

$\Leftrightarrow 6\sqrt{2x+1}-\sqrt{2x+1}-\frac{5}{2}\sqrt{2x+1}+\frac{1}{2}\sqrt{2x+1}=6$

$\Leftrightarrow 3\sqrt{2x+1}=6$

$\Leftrightarrow \sqrt{2x+1}=2$

$\Rightarrow x=\frac{3}{2}$ (thỏa mãn)

23 tháng 10 2020

cảm ơn nha <3

24 tháng 9 2023

a) \(\sqrt{x-1}+\sqrt{4x-4}-\sqrt{25x-25}+2=0\) (ĐK: \(x\ge1\)

\(\Leftrightarrow\sqrt{x-1}+\sqrt{4\left(x-1\right)}-\sqrt{25\left(x-1\right)}+2=0\)

\(\Leftrightarrow\sqrt{x-1}+2\sqrt{x-1}-5\sqrt{x-1}+2=0\)

\(\Leftrightarrow-2\sqrt{x-1}=-2\)

\(\Leftrightarrow\sqrt{x-1}=\dfrac{2}{2}\)

\(\Leftrightarrow\sqrt{x-1}=1\)

\(\Leftrightarrow x-1=1\)

\(\Leftrightarrow x=2\left(tm\right)\)

b) \(\sqrt{16x+16}-\sqrt{9x+9}+\sqrt{4x+4}+\sqrt{x+1}=16\) (ĐK: \(x\ge-1\))

\(\Leftrightarrow\sqrt{16\left(x+1\right)}-\sqrt{9\left(x+1\right)}+\sqrt{4\left(x+1\right)}+\sqrt{x+1}=16\)

\(\Leftrightarrow4\sqrt{x+1}-3\sqrt{x+1}+2\sqrt{x+1}+\sqrt{x+1}=16\)

\(\Leftrightarrow4\sqrt{x+1}=16\)

\(\Leftrightarrow\sqrt{x+1}=4\)

\(\Leftrightarrow x+1=16\)

\(\Leftrightarrow x=15\left(tm\right)\)

AH
Akai Haruma
Giáo viên
28 tháng 6 2019

Lời giải:

a) ĐK: \(x>0; x\neq 25; x\neq 36\)

PT \(\Rightarrow (\sqrt{x}-2)(\sqrt{x}-6)=(\sqrt{x}-5)(\sqrt{x}-4)\)

\(\Leftrightarrow x-8\sqrt{x}+12=x-9\sqrt{x}+20\)

\(\Leftrightarrow \sqrt{x}=8\Rightarrow x=64\) (thỏa mãn)

Vậy.......

b)

ĐK: \(x\geq \frac{-1}{2}\)

PT \(\Leftrightarrow \sqrt{9(2x+1)}-\sqrt{4(2x+1)}+\frac{1}{3}\sqrt{2x+1}=4\)

\(\Leftrightarrow 3\sqrt{2x+1}-2\sqrt{2x+1}+\frac{1}{3}\sqrt{2x+1}=4\)

\(\Leftrightarrow \frac{4}{3}\sqrt{2x+1}=4\Leftrightarrow \sqrt{2x+1}=3\)

\(\Rightarrow x=\frac{3^2-1}{2}=4\) (thỏa mãn)

c)

ĐK: \(x\geq 2\)

PT \(\Leftrightarrow \sqrt{4(x-2)}-\frac{1}{2}\sqrt{x-2}+\sqrt{9(x-2)}=9\)

\(\Leftrightarrow 2\sqrt{x-2}-\frac{1}{2}\sqrt{x-2}+3\sqrt{x-2}=9\)

\(\Leftrightarrow \frac{9}{2}\sqrt{x-2}=9\Leftrightarrow \sqrt{x-2}=2\Rightarrow x=2^2+2=6\) (thỏa mãn)

25 tháng 10 2020

a) \(\frac{3}{4}\sqrt{x}-\sqrt{9x}+5=\frac{1}{4}\sqrt{9x}\)

ĐK : x ≥ 0

⇔ \(\frac{3}{4}\sqrt{x}-\sqrt{3^2x}-\frac{1}{4}\sqrt{3^2x}=-5\)

⇔ \(\frac{3}{4}\sqrt{x}-3\sqrt{x}-\frac{1}{4}\cdot3\sqrt{x}=-5\)

⇔ \(-\frac{9}{4}\sqrt{x}-\frac{3}{4}\sqrt{x}=-5\)

⇔ \(-3\sqrt{x}=-5\)

⇔ \(\sqrt{x}=15\)

⇔ \(x=225\)( tm )

b) \(\sqrt{3-x}-\sqrt{27-9x}+1,25\sqrt{48-16x}=6\)

ĐK : x ≤ 3

⇔ \(\sqrt{3-x}-\sqrt{3^2\left(3-x\right)}+\frac{5}{4}\sqrt{4^2\left(3-x\right)}=6\)

⇔ \(\sqrt{3-x}-3\sqrt{3-x}+\frac{5}{4}\cdot4\sqrt{3-x}=6\)

⇔ \(-2\sqrt{3-x}+5\sqrt{3-x}=6\)

⇔ \(3\sqrt{3-x}=6\)

⇔ \(\sqrt{3-x}=2\)

⇔ \(3-x=4\)

⇔ \(x=-1\)( tm )

c) \(\sqrt{9x^2+12x+4}=4\)

⇔ \(\sqrt{\left(3x+2\right)^2}=4\)

⇔ \(\left|3x+2\right|=4\)

⇔ \(\orbr{\begin{cases}3x+2=4\\3x+2=-4\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=-2\end{cases}}\)

d) \(\frac{1}{3}\sqrt{x-1}+2\sqrt{4x-4}-12\sqrt{\frac{x-1}{25}}=\frac{29}{15}\)

ĐK : x ≥ 1

⇔  \(\frac{1}{3}\sqrt{x-1}+2\sqrt{2^2\left(x-1\right)}-12\sqrt{\left(\frac{1}{5}\right)^2\cdot\left(x-1\right)}=\frac{29}{15}\)

⇔  \(\frac{1}{3}\sqrt{x-1}+2\cdot2\sqrt{x-1}-12\cdot\frac{1}{5}\sqrt{x-1}=\frac{29}{15}\)

⇔  \(\frac{1}{3}\sqrt{x-1}+4\sqrt{x-1}-\frac{12}{5}\sqrt{x-1}=\frac{29}{15}\)

⇔ \(\frac{29}{15}\sqrt{x-1}=\frac{29}{15}\)

⇔ \(\sqrt{x-1}=1\)

⇔ \(x-1=1\)

⇔ \(x=2\)( tm )

23 tháng 8 2021

a, ĐK :a >= 3

\(25\sqrt{\frac{a-3}{25}}-7\sqrt{\frac{4a-12}{9}}-7\sqrt{a^2-9}+18\sqrt{\frac{9a^2-81}{81}}=0\)

\(\Leftrightarrow5\sqrt{a-3}-\frac{14}{3}\sqrt{a-3}-7\sqrt{\left(a-3\right)\left(a+3\right)}+6\sqrt{\left(a-3\right)\left(a+3\right)}=0\)

\(\Leftrightarrow\sqrt{a-3}\left(5-\frac{14}{3}-\sqrt{a+3}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\sqrt{a-3}=0\\\sqrt{a+3}=\frac{1}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}a=3\left(tm\right)\\a=-\frac{2}{9}\left(loai\right)\end{cases}}\)

b, \(ĐK:x\ge-\frac{1}{2}\)

\(\Leftrightarrow3\sqrt{2x+1}-2\sqrt{2x+1}+\frac{1}{3}\sqrt{2x+1}=4\)

\(\Leftrightarrow\frac{4}{3}\sqrt{2x+1}=4\)

\(\Leftrightarrow\sqrt{2x+1}=3\)

\(\Leftrightarrow x=4\left(tm\right)\)

23 tháng 8 2021

a) đk: \(a\ge3\)

pt \(\Leftrightarrow25\frac{\sqrt{a-3}}{\sqrt{25}}-7\frac{\sqrt{4\left(a-3\right)}}{\sqrt{9}}-7\sqrt{a^2-9}+18\frac{\sqrt{9\left(a^2-9\right)}}{\sqrt{81}}=0\)

\(\Leftrightarrow5\sqrt{a-3}-\frac{7.2}{3}\sqrt{a-3}-7\sqrt{a^2-9}+\frac{18.3}{9}\sqrt{a^2-9}=0\)

\(\Leftrightarrow5\sqrt{a-3}-\frac{14}{3}\sqrt{a-3}-7\sqrt{a^2-9}+6\sqrt{a^2-9}=0\)

\(\Leftrightarrow\frac{1}{3}\sqrt{a-3}-\sqrt{a^2-9}=0\)

\(\Leftrightarrow\frac{1}{3}\sqrt{a-3}=\sqrt{a^2-9}\)

\(\Leftrightarrow\frac{1}{9}\left(a-3\right)=a^2-9\)

\(\Leftrightarrow a^2-\frac{1}{9}a-\frac{26}{3}=0\Leftrightarrow\orbr{\begin{cases}a=3\left(tm\right)\\a=-\frac{26}{9}\left(loại\right)\end{cases}}\)

NV
26 tháng 9 2019

ĐKXĐ:

a/ \(x-2020>0\Rightarrow x>2020\)

b/ \(x\ne0\)

c/ \(3x+5< 0\Rightarrow x< -\frac{5}{3}\)

d/ \(\frac{x-3}{1-x}\ge0\Rightarrow1< x\le3\)

Bài 2: ĐKXĐ tự tìm

a/ \(2\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}=28\)

\(\Leftrightarrow13\sqrt{2x}=28\Rightarrow\sqrt{2x}=\frac{28}{13}\)

\(\Rightarrow x=\frac{392}{169}\)

b/ \(2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)

\(\Leftrightarrow\sqrt{x-5}=2\Rightarrow x=9\)

c/ \(3\sqrt{2x+1}>15\Rightarrow\sqrt{2x+1}>5\)

\(\Rightarrow2x+1>25\Rightarrow x>12\)

d/ \(\sqrt{x}+1>12\Rightarrow\sqrt{x}>11\Rightarrow x>121\)

17 tháng 1 2017

Nhìn không đủ chán rồi không dám động vào

17 tháng 1 2017

Viết đề kiểu gì v @@