Question

Cho biểu thức:

  

Answer 1

1: \(B=\dfrac{y+\sqrt{y}-3+\sqrt{y}+3}{y-9}=\dfrac{y+2\sqrt{y}}{y-9}\)

2: B>1

=>B-1>0

=>\(\dfrac{y+2\sqrt{y}-y+9}{y-9}>0\)

=>\(\dfrac{2\sqrt{y}+9}{y-9}>0\)

=>y-9>0

=>y>9

Answer 2

\(B=\dfrac{y}{y-9}+\dfrac{1}{\sqrt{y}+3}+\dfrac{1}{\sqrt{y}-3}\left(Đk:y\ge0;y\ne9\right)\)

\(=\dfrac{y+\sqrt{y}-3+\sqrt{y}+3}{y-9}\)

\(=\dfrac{y+2\sqrt{y}}{y-9}\)

\(B>1\Rightarrow\dfrac{y+2\sqrt{y}}{y-9}>1\)

\(\Rightarrow\dfrac{y+2\sqrt{y}-y+9}{y-9}>0\)

\(\Leftrightarrow\dfrac{2\sqrt{y}+9}{y-9}>0\)

\(\Leftrightarrow y>9\left(2\sqrt{y}+9>0\right)\)