Question

Tìm GTNN của biểu thức

A=2x^2+4x

Answer 1

Giúp mình với

Answer 2

A = 2x² +4x

⇒ A= 2x² +4x + 2 - 2

⇒A = 2(x² +2x + 1) - 2

⇒A = 2(x+1)² -2 ≥ -2

Dấu "=" xảy ra khi và chỉ khi:

(x+1)² = 0

⇒ x + 1 = 0 ⇒ x = -1

Answer 3

\(2x^2+4x\)

\(=2\left(x^2+x\right)=2\left(x^2+2x\dfrac{1}{2}+\dfrac{1}{4}\right)-\dfrac{1}{2}\)

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

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

\(\Rightarrow min=\dfrac{-1}{2}\Leftrightarrow x-\dfrac{1}{2}=0\Rightarrow x=\dfrac{1}{2}\)

Answer 4

mk sai lm lại nek

\(2x^2+4x=2\left(x^2+2x+1\right)-2=2\left(x+1\right)^2-1\)

\(2\left(x^2+1\right)\ge0\Rightarrow2\left(x^2+1\right)-2\ge-2\)\(\Rightarrow min=-2\Leftrightarrow x+1=0\Rightarrow x=-1\)