Question

Giải phương trình

a) \(\sqrt{7x-14}=5\)

b) \(\sqrt{x^2-25}-\sqrt{x-5}=0\)

c) \(x-5\sqrt{x-2}=-2\)

Answer 1

a) \(\sqrt{7x-14}=5\)

\(\Leftrightarrow\left(\sqrt{7x-14}\right)^2=25\)

\(\Leftrightarrow\left|7x-14\right|=25\)

*Nếu \(7x-14\ge0\Rightarrow x\ge2\)

\(7x-14=25\Rightarrow x=\dfrac{39}{7}\left(TMĐK\right)\)

*Nếu \(7x-14< 0\Rightarrow x< 2\)

\(14-7x=25\Rightarrow x=-\dfrac{10}{7}\left(TMĐK\right)\)

Answer 2

b: \(\Leftrightarrow\sqrt{x-5}\left(\sqrt{x+5}-1\right)=0\)

=>x-5=0 hoặc x+5=1

=>x=5 hoặc x=-4(loại)

c: \(\Leftrightarrow\sqrt{25x-50}=x+2\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-2\\x^2+4x+4-25x+50=0\end{matrix}\right.\Leftrightarrow x\in\left\{3;18\right\}\)