Question

1. tính giá trị lớn nhất của mỗi biểu thức

A=10-(\(\left(y^2-25\right)^4\)

B= (-125)- \(\left(x-4\right)^2\)-\(\left(y-5\right)^2\)

Answer 1

a/ Với mọi y ta có :

\(\left(y^2-25\right)^4\ge0\)

\(\Leftrightarrow-\left(y^2-25\right)^4\le0\)

\(\Leftrightarrow10-\left(y^2-25\right)^4\le10\)

\(\Leftrightarrow A\le10\)

Dấu "=" xảy ra :

\(\Leftrightarrow\left(y^2-25\right)^4=0\)

\(\Leftrightarrow\left[{}\begin{matrix}y=5\\y=-5\end{matrix}\right.\)

Vậy...

b/ Với mọi x, y ta có :

\(\left\{{}\begin{matrix}\left(x-4\right)^2\ge0\\\left(y-5\right)^2\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}-\left(x-4\right)^2\le0\\-\left(y-5\right)\le0\end{matrix}\right.\)

\(\Leftrightarrow-\left(x-4\right)-\left(y-5\right)^2\le0\)

\(\Leftrightarrow-125-\left(x-4\right)^2-\left(y-5\right)^2\le-125\)

\(\Leftrightarrow B\le-125\)

Dấu "=" xảy ra

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-4\right)^2=0\\\left(y-5\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=5\end{matrix}\right.\)

Vậy..