Question

Tìm GTNN của:

P=\(\left|x-2018\right|+2019\)

R=\(\left|2.x-4\right|+\left|2.x+5\right|+1\)

Q=\(\left|x+\dfrac{1}{3}\right|+\left|x-\dfrac{2}{3}\right|\)

Answer 1

1) Vì \(\left|x-2018\right|\) \(\ge\) \(\forall\) x \(\in\) Z
=> \(\left|x-2018\right|+2019\) \(\ge\) 2019
Vậy để biểu thức đạt GTNN \(\Leftrightarrow\)\(\left|x-2018\right|\) = 0
=> x - 2018 = 0
=> x = 0 + 2018
=> x = 2018
Thay x vào biểu thức, ta có:
\(\left|2018-2018\right|\) + 2019
= 0 + 2019
= 2019

Answer 2

R=|2x-4|+|2x+5|+1

=|4-2x|+|2x+5|+1

=>R>=|4-2x+2x+5|+1=10

Dấu = xảy ra khi (2x-4)(2x+5)<=0

=>-5/2<=x<=2

c: Q=|x+1/3|+|2/3-x|>=|x+1/3+2/3-x|=1

Dấu = xảy ra khi (x+1/3)(x-2/3)<=0

=>-1/3<=x<=2/3