Question Number 224455 by AgniMath last updated on 13/Sep/25
$${If}\:{a},{b},{c}\:\neq\:\mathrm{0}\:{what}\:{is}\:{the}\:{difference} \\ $$$${between}\:{the}\:{maximum}\:{snd}\:{minimum}\: \\ $$$${value}\:{of} \\ $$$${S}\:=\:\mathrm{1}\:+\:\frac{\mid{a}\mid}{{a}}\:+\:\frac{\mathrm{2}\mid{b}\mid}{{b}}\:+\:\frac{\mathrm{3}\mid{ab}\mid}{{ab}}\:−\:\frac{\mathrm{4}\mid{c}\mid}{{c}}\:? \\ $$
Answered by mr W last updated on 13/Sep/25
$${S}_{{max}} =\mathrm{1}+\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}=\mathrm{11} \\ $$$${S}_{{min}} =\mathrm{1}+\mathrm{1}−\mathrm{2}−\mathrm{3}−\mathrm{4}=−\mathrm{7} \\ $$$${S}_{{max}} −{S}_{{min}} =\mathrm{18} \\ $$