a) \(\left\{{}\begin{matrix}x\ge0\\x\ne\dfrac{5}{3}\end{matrix}\right.\)

b) \(x\ne\dfrac{1}{2}\)

c) \(\left[{}\begin{matrix}x>\dfrac{1}{2}\\x< -5\end{matrix}\right.\)

thay cái ảnh nền giùm cái !!!!

Nhỏ quá

cái dưới á ...

a: Xét tứ giác ABHK có 

\(\widehat{AHB}=\widehat{AKB}=90^0\)

Do đó: ABHK là tứ giác nội tiếp

Bài 2:

ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >9\end{matrix}\right.\)

Để A là số nguyên thì \(\sqrt{x}+1⋮\sqrt{x}-3\)

=>\(\sqrt{x}-3+4⋮\sqrt{x}-3\)

=>\(4⋮\sqrt{x}-3\)

=>\(\sqrt{x}-3\in\left\{1;-1;2;-2;4;-4\right\}\)

=>\(\sqrt{x}\in\left\{4;2;5;1;7;-1\right\}\)

=>\(\sqrt{x}\in\left\{1;2;4;5;7\right\}\)

=>\(x\in\left\{1;4;16;25;49\right\}\)

Bài 5:

a) Ta có: \(\left(x-3\right)^2=11+6\sqrt{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=-3-\sqrt{2}\\x-3=3+\sqrt{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\sqrt{2}\\x=6+\sqrt{2}\end{matrix}\right.\)

c) Ta có: \(x^2-10x+25=27-10\sqrt{2}\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-5=\sqrt{2}-5\\x-5=5-\sqrt{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=10-\sqrt{2}\end{matrix}\right.\)

Bài 6: 

c) Ta có: \(\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+...+\sqrt{1+\dfrac{1}{2021^2}+\dfrac{1}{2022^2}}\)

\(=\dfrac{1}{1}+\dfrac{1}{2}-\dfrac{1}{3}+1+\dfrac{1}{3}-\dfrac{1}{4}+...+1+\dfrac{1}{2021}-\dfrac{1}{2022}\)

\(=98+\dfrac{1}{2}-\dfrac{1}{2022}\)

\(\simeq98.5\)

anh giúp em bài 2 luôn vs