Question

tìm GTNN của biểu thức

a/ A = \(x^2-3x+1\)

b/ B = \(x^2+2xy+2y+2y^2+2\)

Answer 1

a) A=x²-3x+1

A= x²-2.x.\(\dfrac{3}{2}\) +\(\dfrac{9}{4}\) +1-\(\dfrac{9}{4}\)

A=(x²-2.x.\(\dfrac{3}{2}\) +\(\dfrac{9}{4}\) )-\(\dfrac{5}{4}\)

A=(x-\(\dfrac{3}{2}\) )²- \(\dfrac{5}{4}\)

\(Do\left(x-\dfrac{3}{2}\right)^2\ge0\forall x\)

=>\(\left(x-\dfrac{3}{2}\right)^2-\dfrac{5}{4}\ge-\dfrac{5}{4}\)

=>A\(\ge-\dfrac{5}{4}\)

vậy GTNN của A= -\(\dfrac{5}{4}\) khi

\(x-\dfrac{5}{4}=0\)

<=>x=\(\dfrac{5}{4}\)