Question

Tìm GTNN của biểu thức :

C = 4x² - 8x + 100 .

D = |x| + 5 + ( -155 - \(\dfrac{2}{5}\) )

Answer 1

Giải:

a) \(C=4x^2-8x+100\)

\(\Leftrightarrow C=4x^2-8x+4+96\)

\(\Leftrightarrow C=\left(4x^2-8x+4\right)+96\)

\(\Leftrightarrow C=\left(2x-2\right)^2+96\ge96;\forall x\)

\(\Leftrightarrow C_{Min}=96\)

\("="\Leftrightarrow2x-2=0\Leftrightarrow x=1\)

Vậy ...

b) \(D=\left|x\right|+5+\left(-155-\dfrac{2}{5}\right)\)

\(\Leftrightarrow D=\left|x\right|+5-155-\dfrac{2}{5}\)

\(\Leftrightarrow D=\left|x\right|-150-\dfrac{2}{5}\)

\(\Leftrightarrow D=\left|x\right|-150,4\ge-150,4;\forall x\)

\(\Leftrightarrow D_{Min}=-150,4\)

\("="\Leftrightarrow\left|x\right|=0\Leftrightarrow x=0\)

Vậy ...