Toán Lớp 9: M=( √x/ √x-1-1/x- √x)÷(1/ √x+1+2/x-1)
b. Tính x sao cho M>0
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: M=( √x/ √x-1-1/x- √x)÷(1/ √x+1+2/x-1)
b. Tính x sao cho M>0
Comments ( 1 )
Dkxd:x > 0;x\# 1\\
M = \left( {\dfrac{{\sqrt x }}{{\sqrt x – 1}} – \dfrac{1}{{x – \sqrt x }}} \right):\left( {\dfrac{1}{{\sqrt x + 1}} + \dfrac{2}{{x – 1}}} \right)\\
= \dfrac{{\sqrt x .\sqrt x – 1}}{{\sqrt x \left( {\sqrt x – 1} \right)}}:\dfrac{{\sqrt x – 1 + 2}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x – 1} \right)}}\\
= \dfrac{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x \left( {\sqrt x – 1} \right)}}.\dfrac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x – 1} \right)}}{{\sqrt x + 1}}\\
= \dfrac{{x – 1}}{{\sqrt x }}\\
M > 0\\
\Leftrightarrow M > 0\\
\Leftrightarrow \dfrac{{x – 1}}{{\sqrt x }} > 0\\
\Leftrightarrow x – 1 > 0\\
\Leftrightarrow x > 1\\
Vay\,x > 1
\end{array}$