Question

[Bảo Ngọc]

Giúp em mấy câu này với ạ

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(\sqrt{2x+3}=5\)

\(\Leftrightarrow2x+3=25\)

hay x=11

b: \(\sqrt{\left(x-2\right)^2}=8\)

\(\Leftrightarrow\left|x-2\right|=8\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.\)

Answer 2

[Lấp La Lấp Lánh]

a) \(\sqrt{3+2x}=5\left(đk:x\ge-\dfrac{3}{2}\right)\)

\(\Leftrightarrow3+2x=25\Leftrightarrow x=11\left(tm\right)\)

b) \(\sqrt{\left(x-2\right)^2}=8\)

\(\Leftrightarrow\left|x-2\right|=8\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.\)

c) \(đk:x\le3\)

\(\Leftrightarrow\sqrt{3-x}-3\sqrt{3-x}+5\sqrt{3-x}=6\)

\(\Leftrightarrow3\sqrt{3-x}=6\)

\(\Leftrightarrow\sqrt{3-x}=2\Leftrightarrow3-x=4\Leftrightarrow x=-1\left(tm\right)\)

d) \(đk:x\ge0\)

\(\Leftrightarrow4\sqrt{x}-6\sqrt{x}+4\sqrt{x}=5\)

\(\Leftrightarrow2\sqrt{x}=5\Leftrightarrow\sqrt{x}=\dfrac{5}{2}\Leftrightarrow x=\dfrac{25}{4}\left(tm\right)\)

e) \(đk:x\ge-5\)

\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)

\(\Leftrightarrow3\sqrt{x+5}=6\Leftrightarrow\sqrt{x+5}=2\Leftrightarrow x+5=4\Leftrightarrow x=-1\left(tm\right)\)

f) \(đk:x\ge-2\)

\(\Leftrightarrow3\sqrt{x+2}-5\sqrt{x+2}+4\sqrt{x+2}=6\)

\(\Leftrightarrow2\sqrt{x+2}=6\Leftrightarrow\sqrt{x+2}=3\Leftrightarrow x+2=9\Leftrightarrow x=7\left(tm\right)\)