Toán Lớp 8: tìm x,y,z tm pt sau:
$4{{x}^{2}}+2{{y}^{2}}+2{{z}^{2}}+4xy-2yz+2y-10z+17=0$
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 8: tìm x,y,z tm pt sau:
$4{{x}^{2}}+2{{y}^{2}}+2{{z}^{2}}+4xy-2yz+2y-10z+17=0$
Comments ( 1 )
$\Leftrightarrow \left( 4{{x}^{2}}+4xy+{{y}^{2}} \right)+\left[ {{y}^{2}}-2y.\left( z-1 \right)+{{\left( z-1 \right)}^{2}} \right]+\left( {{z}^{2}}-8z+16 \right)=0$
$\Leftrightarrow {{\left( 2x+y \right)}^{2}}+{{\left( y-z+1 \right)}^{2}}+{{\left( z-4 \right)}^{2}}=0$
$\Leftrightarrow\begin{cases}2x+y=0\\y-z+1=0\\z-4=0\end{cases}$
$\Leftrightarrow\begin{cases}x=-\dfrac{3}{2}\\y=3\\z=4\end{cases}$