Question

giải phương trình : \(\frac{5}{x-4\sqrt{x}+5}-x+4\sqrt{x}-1=0\)

Answer 1

ta có Pt

<=> \(\frac{5}{x-4\sqrt{x}+5}-x+4\sqrt{x}-5+4=0\)

đặt \(x-4\sqrt{x}+5=a\Rightarrow PT\Leftrightarrow\frac{5}{a}-a+4=0\)

<=>\(5-a^2+4a=0\Leftrightarrow a^2-4a-5=0\Leftrightarrow\left(a-5\right)\left(a+1\right)=0\)

<=>a=5\(\Leftrightarrow x-4\sqrt{x}+5=5\Leftrightarrow x-4\sqrt{x}=0\Leftrightarrow\sqrt{x}\left(\sqrt{x}-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=16\end{cases}}\)