Question

Bài 1: Tìm x;

a)√x+5+√9x+45+√9+45=10

b)√x2−4x+4=√3+2√2

Answer 1

a: \(\Leftrightarrow\sqrt{x+5}+3\sqrt{x+5}+\sqrt{54}=10\)

\(\Leftrightarrow4\sqrt{x+5}=10-\sqrt{54}\)

\(\Leftrightarrow x+5=\left(\dfrac{10-\sqrt{54}}{4}\right)^2=\dfrac{77-30\sqrt{6}}{5}\)

hay \(x=\dfrac{52-30\sqrt{6}}{5}\)

b: \(\Leftrightarrow\left|x-2\right|=\left|\sqrt{2}+1\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=\sqrt{2}+1\\x-2=-\sqrt{2}-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3+\sqrt{2}\\x=1-\sqrt{2}\end{matrix}\right.\)