Toán Lớp 8: Bài 2 : tìm gtnn của
A=x^2.2x+5
B=x^2+y^2-x+6y-10
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: Bài 2 : tìm gtnn của
A=x^2.2x+5
B=x^2+y^2-x+6y-10
Comments ( 2 )
a)A = {x^2} + 2x + 5\\
= {x^2} + 2x + 1 + 4\\
= {\left( {x + 1} \right)^2} + 4 \ge 4\\
\Leftrightarrow GTNN:A = 4\,khi:x = – 1\\
A = {x^2} – 2x + 5\\
= {\left( {x – 1} \right)^2} + 4 \ge 4\\
\Leftrightarrow GTNN:A = 4\,khi:x = 1\\
b)\\
B = {x^2} + {y^2} – x + 6y – 10\\
= {x^2} – x + \dfrac{1}{4} + {y^2} + 6y + 9 – \dfrac{{77}}{4}\\
= {x^2} – 2.x.\dfrac{1}{2} + \dfrac{1}{4} + {\left( {y + 3} \right)^2} – \dfrac{{77}}{4}\\
= {\left( {x – \dfrac{1}{2}} \right)^2} + {\left( {y + 3} \right)^2} – \dfrac{{77}}{4} \ge \dfrac{{ – 77}}{4}\\
\Leftrightarrow B \ge \dfrac{{ – 77}}{4}\\
\Leftrightarrow GTNN:B = \dfrac{{ – 77}}{4}\,khi:\left\{ \begin{array}{l}
x = \dfrac{1}{2}\\
y = – 3
\end{array} \right.
\end{array}$