$H=|2x-3,15|+|2x-8,07|$
$⇒H=|2x-3,15|+|8,07-2x|$
Áp dụng tính chất $|a| + |b| ≥ |a+b|$ dấu $"="$ khi $a.b≥0$
$⇒ H =|2x-3,15|+|2x-8,07| ≥ |2x - 3,15 + 8,07 - 2x| = 4,92$
$⇒ H ≥ 4,92$ $∀$ $x$
Để $H=4,92$ thì $(2x-3,15)(8,07 - 2x) ≥0$ hay $2x-3,15$ cùng dấu với $8,07-2x$
$TH1$$\left \{ {{2x-3,15>0} \atop {8,07-2x>0}} \right.$ $⇔$ $\left \{ {{2x>3,15} \atop {2x<8,07}} \right.$ $⇔$ $\left \{ {{x>1,575} \atop {x<4,035}} \right.$ $⇔$ $1,575 < x < 4,035$ ($TM$)
$TH2$$\left \{ {{2x-3,15>0} \atop {8,07-2x<0}} \right.$ $⇔$ $\left \{ {{2x<3,15} \atop {2x>8,07}} \right.$ $⇔$ $\left \{ {{x<1,575} \atop {x>4,035}} \right.$ $⇔$ $KTM$
$TH3$$\left \{ {{2x-3,15=0} \atop {8,07-2x=0}} \right.$ $⇔$ $\left \{ {{x=1,575} \atop {x=4,035}} \right.$
Vậy $1,575 ≤ x ≤ 4,035$ thì $H$ đạt $GTNN=4,92$.
