Question

tìm x

1) \(\sqrt{\left(x-4\right)^2}\) = 5

2) \(\sqrt{4x-4}\) + \(\sqrt{25\left(x-1\right)}\) - \(\sqrt{\frac{1}{4}\left(x-1\right)}\) = 5 - \(\sqrt{x-1}\)

Answer 1

1, ĐKXĐ:\(x\)∈R

PT⇔\(\left|x-4\right|=5\)⇔\(\left[{}\begin{matrix}x-4=5\\x-4=-5\end{matrix}\right.\)⇔\(\left[{}\begin{matrix}x=9\\x=-1\end{matrix}\right.\)

Answer 2

2. ĐKXĐ:\(x\)≥1

PT⇔ \(2\sqrt{x-1}+5\sqrt{x-1}-\frac{1}{2}\sqrt{x-1}+\sqrt{x-1}=5\)

⇔ \(\frac{15}{2}\sqrt{x-1}=5\)⇔\(3\sqrt{x-1}=2\)⇔\(9\left(x-1\right)=4\)⇔\(x=\frac{13}{9}\)(thỏa mãn)