Toán Lớp 9: Cho P=(x+√x+1)/√x.Hãy so sánh P với 3
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 9: Cho P=(x+√x+1)/√x.Hãy so sánh P với 3
Comments ( 1 )
Dkxd:x > 0\\
P – 3\\
= \dfrac{{x + \sqrt x + 1}}{{\sqrt x }} – 3\\
= \dfrac{{x + \sqrt x + 1 – 3\sqrt x }}{{\sqrt x }}\\
= \dfrac{{x – 2\sqrt x + 1}}{{\sqrt x }}\\
= \dfrac{{{{\left( {\sqrt x – 1} \right)}^2}}}{{\sqrt x }}\\
Do:\left\{ \begin{array}{l}
{\left( {\sqrt x – 1} \right)^2} \ge 0\\
\sqrt x > 0
\end{array} \right.\\
\Leftrightarrow \dfrac{{{{\left( {\sqrt x – 1} \right)}^2}}}{{\sqrt x }} \ge 0\\
\Leftrightarrow P \ge 3\\
Vay\,P \ge 3
\end{array}$