Question

Tìm x để M = N (biết \(M=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}\), \(N=\dfrac{2}{\sqrt{x}-1}\))

Answer 1

\(M=N\Leftrightarrow\dfrac{\sqrt{x}+1}{\sqrt{x}-2}=\dfrac{2}{\sqrt{x}-1}\)

\(\Rightarrow\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)=2\left(\sqrt{x}-2\right)\)

\(\Rightarrow x-1=2\left(\sqrt{x}-2\right)\)

\(\Rightarrow x-1=2\sqrt{x}-4\)

\(\Rightarrow x=2\sqrt{x}-3\)

\(\Rightarrow x-2\sqrt{x}+3=0\)

\(\Rightarrow x-2\sqrt{x}+1+2=0\)

\(\Rightarrow\left(\sqrt{x}-1\right)^2+2=0\)

\(x\in\varnothing\)