Question

Answer 1

1.

\(A=\sqrt{\left(x-4\right)^2+2}-12\ge\sqrt{2}-12\)

\(A_{min}=\sqrt{2}-12\) khi \(x=4\)

\(B=\sqrt{\left(x-y+1\right)^2+4}+2\left(y-2\right)^2+2010\ge\sqrt{4}+2010=2012\)

\(B_{min}=2012\) khi \(\left(x;y\right)=\left(1;2\right)\)

2.

\(2x^2\ge0\Rightarrow3-2x^2\le3\Rightarrow A\le\sqrt{3}\)

\(A_{max}=\sqrt{3}\) khi \(x=0\)

\(B=5+\sqrt{1-\left(2x+1\right)^2}\le5+\sqrt{1}=6\)

\(B_{max}=6\) khi \(x=-\dfrac{1}{2}\)