Question

Ai giải giúp em câu 2 vs 3 đi

Answer 1

2.
a) Đkxđ \(x\ge2\).
\(5\sqrt{x-2}=10+\sqrt{9x-18}\)
\(\Leftrightarrow5\sqrt{x-2}=10+\sqrt{9\left(x-2\right)}\)
\(\Leftrightarrow5\sqrt{x-2}=10+3\sqrt{x-2}\)
\(\Leftrightarrow2\sqrt{x-2}=10\)
\(\Leftrightarrow\sqrt{x-2}=5\)
\(\Leftrightarrow x-2=5^2\)
\(\Leftrightarrow x=27\).
b)
\(\sqrt{\left(2x-1\right)^2}=5\)
\(\Leftrightarrow\left|2x-1\right|=\sqrt{5}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=\sqrt{5}\\2x-1=-\sqrt{5}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\sqrt{5}+1\\2x=-\sqrt{5}+1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\sqrt{5}+1}{2}\\x=\dfrac{-\sqrt{5}+1}{2}\end{matrix}\right.\)