\(-\dfrac{4}{5}\sqrt{50-25x}-\dfrac{2}{3}\sqrt{18-9x}+6=0\left(x\le2\right)\\ \Leftrightarrow-\dfrac{4}{5}\cdot5\sqrt{2-x}-\dfrac{2}{3}\cdot3\sqrt{2-x}=-6\\ \Leftrightarrow-2\sqrt{2-x}=-6\\ \Leftrightarrow\sqrt{2-x}=3\Leftrightarrow2-x=9\\ \Leftrightarrow x=-7\left(tm\right)\)

Lần sau bạn nhớ ghi đúng đề nhé!

\(\sqrt{25x+75}+3\sqrt{x-2}=2+4\sqrt{x+3}-\sqrt{9x-18}\)

Đk: \(x\ge2\)

pt <=> \(\sqrt{25\left(x+3\right)}+3\sqrt{x-2}=2+4\sqrt{x+3}-\sqrt{9\left(x-2\right)}\)

\(\Leftrightarrow5\sqrt{x+3}+3\sqrt{x-2}=2+4\sqrt{x+3}-3\sqrt{x-2}\)

\(\Leftrightarrow\sqrt{x+3}+6\sqrt{x-2}=2\)

\(\Leftrightarrow x+3+36\left(x-2\right)+12\sqrt{\left(x+3\right)\left(x-2\right)}=4\)

\(\Leftrightarrow12\sqrt{x^2+x-6}=73-37x\)

phương trình vô nghiệm vì \(x\ge2\Rightarrow73-37x< 0\)mà \(VT\ge0\)

\(35^2\)= 1225

x = 1225:25 = 49

Vậy x = 49

căn 25 x =35 

25 x =35^2

suyra x=49

Ta có : \(\sqrt{25.x}=35\)

\(\Rightarrow\sqrt{5^2.x}=35\)

\(\Rightarrow\sqrt{5^2}.\sqrt{x}=35\)

\(\Rightarrow\sqrt{x}=35:5\)

\(\Rightarrow\sqrt{x}=7\)

\(\Rightarrow\sqrt{x}=7\) hoặc \(-\sqrt{x}=-7\)

\(\Rightarrow x=49\) hoặc  \(x=-49\)

ĐKXĐ: \(x\ge2\)

\(\dfrac{2}{5}\sqrt{25x-50}=6\)

\(\Leftrightarrow\dfrac{2}{5}\sqrt{25\left(x-2\right)}=6\)

\(\Leftrightarrow2\sqrt{x-2}=6\Leftrightarrow\sqrt{x-2}=3\)

\(\Leftrightarrow x-2=9\Leftrightarrow x=11\left(tm\right)\)

\(ĐK:x\ge2\\ PT\Leftrightarrow\dfrac{2}{5}\cdot5\sqrt{x-2}=6\\ \Leftrightarrow2\sqrt{x-2}=6\Leftrightarrow\sqrt{x-2}=3\\ \Leftrightarrow x-2=9\\ \Leftrightarrow x=11\left(tm\right)\)

\(\dfrac{2}{5}\sqrt{25x-50}=6\)

\(\Leftrightarrow\dfrac{2}{5}\sqrt{25\left(x-2\right)}=6\)

\(\Leftrightarrow2\sqrt{x-2}=6\)

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

\(\Leftrightarrow x-2=9\)

\(\Leftrightarrow x=11\)

\(\sqrt{25x}\ge0\)

⇒\(25x\ge0\)

⇔\(x\ge0\)

⇒

⇔

\(2,\\ a,\sqrt{4x-4}+\sqrt{9x-9}-\sqrt{25x-25}=7\left(x\ge1\right)\\ \Leftrightarrow2\sqrt{x-1}+3\sqrt{x-1}-5\sqrt{x-1}=7\\ \Leftrightarrow0\sqrt{x-1}=7\Leftrightarrow x\in\varnothing\\ b,\sqrt{2x^2-3}=4\left(x\le-\dfrac{\sqrt{6}}{2};\dfrac{\sqrt{6}}{2}\le x\right)\\ \Leftrightarrow2x^2-3=16\\ \Leftrightarrow x^2=\dfrac{19}{2}\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{19}{2}}\left(tm\right)\\x=-\sqrt{\dfrac{19}{2}}\left(tm\right)\end{matrix}\right.\)

\(1,\\ A=\sqrt{5+4x}+\sqrt{7-3x}\\ ĐKXĐ:\left\{{}\begin{matrix}5+4x\ge0\\7-3x\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{5}{4}\\x\le\dfrac{7}{3}\end{matrix}\right.\)

Bài 2:

a) \(\sqrt{4x-4}+\sqrt{9x-9}-\sqrt{25x-25}=7\left(đk:x\ge1\right)\)

\(\Leftrightarrow2\sqrt{x-1}+3\sqrt{x-2}-5\sqrt{x-1}=7\)

\(\Leftrightarrow0=7\left(VLý\right)\)

Vậy \(S=\varnothing\)

b) \(\sqrt{2x^2-3}=4\left(đk:-\sqrt{\dfrac{3}{2}}\ge x\ge\sqrt{\dfrac{3}{2}}\right)\)

\(\Leftrightarrow2x^2-3=16\)

\(\Leftrightarrow2x^2=19\Leftrightarrow x^2=\dfrac{19}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{19}{2}}\left(tm\right)\\x=-\sqrt{\dfrac{19}{2}}\left(tm\right)\end{matrix}\right.\)

Bài 2

a . \(\sqrt{x-1}=3\Leftrightarrow x-1=9\Leftrightarrow x=10\)

b . \(\sqrt{x^2-6x+9}=1\Leftrightarrow\sqrt{\left(x-3\right)^2}=1\Leftrightarrow x-3=1\Leftrightarrow x=4\)

c . \(\sqrt{25x^2-10x+1}=5\Leftrightarrow\sqrt{\left(5x-1\right)^2}=5\Leftrightarrow5x-1=5\Leftrightarrow x=\frac{6}{5}\)

Bài 1

\(\sqrt{2}+\sqrt{3}+\sqrt{8}+\frac{\sqrt{16}}{\sqrt{2}}+\sqrt{3}+\sqrt{4}=\sqrt{2}+2\sqrt{3}+2\sqrt{2}+2\sqrt{2}+2\)

\(=5\sqrt{2}+2\sqrt{3}+2\)