Question

Tìm GTNN của biểu thức

A=2x^2+2x+1

Answer 1

Giúp mình với mình đang cần gấp

Answer 2

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

=2(x+\(\dfrac{1}{2}\) )² -\(\dfrac{1}{2}\)

Answer 3

\(A=2x^2+2x+1=2\left(x^2+x+\dfrac{1}{2}\right)=2\left[\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{1}{4}\right]=2\left[\left(x+\dfrac{1}{2}\right)^2+\dfrac{1}{4}\right]=2\left(x+\dfrac{1}{2}\right)^2+\dfrac{1}{2}\)

Vì: \(2\left(x+\dfrac{1}{2}\right)^2\ge0\forall x\Rightarrow2\left(x+\dfrac{1}{2}\right)^2+\dfrac{1}{2}\ge\dfrac{1}{2}\)

Dấu ''='' xảy ra khi \(x=-\dfrac{1}{2}\)

Vậy \(MIN_A=\dfrac{1}{2}\Leftrightarrow x=-\dfrac{1}{2}\)