Question

Giải pt sau:

\(\dfrac{\sqrt{x}-2}{\sqrt{x}-5}=\dfrac{\sqrt{x}-4}{\sqrt{x}-6}\)

Answer 1

\(\Leftrightarrow\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-6\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-6\right)}=\dfrac{\left(\sqrt{x}-4\right)\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-6\right)}\)

\(\Leftrightarrow\dfrac{x-8\sqrt{x}+12}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-6\right)}-\dfrac{x-9\sqrt{x}+20}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-6\right)}=0\)

\(\Leftrightarrow\dfrac{x-8\sqrt{x}+12-x+9\sqrt{x}-20}{\left(\sqrt{x}-5\right)\left(\sqrt{x}-6\right)}=0\)

\(\Leftrightarrow\sqrt{x}-8=0\)

\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{8}\\x=-\sqrt{8}\end{matrix}\right.\)