Question

Cho P=\((\dfrac{\sqrt{x}}{2}-\dfrac{1}{2\sqrt{x}})^2\).\((\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1})\)

a)Tìm ĐKXĐ.Rút gọn P

b)Tìm x để P<0

Answer 1

a. ĐKXĐ: \(x>0;x\ne1\)

\(P=\left(\dfrac{\sqrt{x}}{2}-\dfrac{1}{2\sqrt{x}}\right)^2\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right)\)

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

\(=\dfrac{\left(x-1\right)^2}{4x}.\dfrac{-4\sqrt{x}}{x-1}=\dfrac{1-x}{\sqrt{x}}\)

b.

\(P< 0\Rightarrow\dfrac{1-x}{\sqrt{x}}< 0\Rightarrow1-x< 0\)

\(\Rightarrow x>1\)