Question

Tìm GTNN hoac GTLN cua bieu thuc sau

4x² + 4x + 11

Answer 1

Answer 2

\(A=4x^2+4x+11=\left(4x^2+4x+1\right)+10\)

\(=\left(2x+1\right)^2+10\)

Vì \(\left(2x+1\right)^2\ge0\forall x\Rightarrow\left(2x+1\right)^2+10\ge10\)

''='' xảy ra khi \(x=-\dfrac{1}{2}\)

Vậy Min_A = 10 khi x = -1/2

Answer 3

\(A=4x^2+4x+11\)

\(\Leftrightarrow A=4x^2+4x+1+10\)

\(\Leftrightarrow A=\left[\left(2x\right)^2+2.2x+1\right]+10\)

\(\Leftrightarrow A=\left(2x+1\right)^2+10\)

Vậy GTNN của A=10 khi \(2x+1=0\Leftrightarrow x=\dfrac{-1}{2}\)