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: \(\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+...+\sqrt{1+\dfrac{1}{2021^2}+\dfrac{1}{2022^2}}\)
\(=\dfrac{1}{1}+\dfrac{1}{2}-\dfrac{1}{3}+1+\dfrac{1}{3}-\dfrac{1}{4}+...+1+\dfrac{1}{2021}-\dfrac{1}{2022}\)
\(=98+\dfrac{1}{2}-\dfrac{1}{2022}\)
\(\simeq98.5\)
