Question

Answer 1

a) \(A=\left(x-y\right)^2+1=\left(2,009-0,009\right)^2+1=2^2+1=5\)

b) \(A=\left(x-y\right)^2+1\ge1>0\forall x,y\in R\)

c) \(A=\left(x-y\right)^2+1\ge1\)

\(minA=1\Leftrightarrow x=y\)

Bài 2:

a) \(A=2\left(x^2-4x+4\right)+2=2\left(x-2\right)^2+2\ge2\)

\(minA=2\Leftrightarrow x=2\)

b) \(B=\dfrac{3\left(x^2+2x+3\right)+1}{x^2+2x+3}=3+\dfrac{1}{\left(x^2+2x+1\right)+2}=3+\dfrac{1}{\left(x+1\right)^2+2}\le3+\dfrac{1}{2}=\dfrac{7}{2}\)

\(maxB=\dfrac{7}{2}\Leftrightarrow x=-1\)