Question

Answer 1

\(a,A=\left|2x-1\right|+5\ge5\\ A_{min}=5\Leftrightarrow2x-1=0\Leftrightarrow x=\dfrac{1}{2}\\ b,B=2015+\left|2014-2x\right|\ge2015\\ A_{min}=2015\Leftrightarrow2014-2x=0\Leftrightarrow x=1007\)

Answer 2

A=|2x-1|+5

 | 2 x − 1 | ≥ 0

⇔ A = | 2 x − 1 | + 5 ≥ 5

Để A đạt GTNN thì | 2 x − 1 |đạt GTNN

 Dấu "=" xảy ra khi :

| 2 x − 1 | = 0

⇔2x−1=0

⇔ 2 x = 1

⇔ x = 1/ 2

⇔x=1/2

Vậy A đạt GTNN = 5 khi x = 1/ 2

Answer 3

B=2015+|2014-2x|

Ta có :

|2014−2x|≥0

⇔B=2015+|2014−2x|≥2015

Dấu "=" xảy ra khi :

|2014−2x|=0

⇔2014−2x=0

⇔2x=2014

⇔x=1007

Vậy B đạt GTNN = 2015 khi x = 1007