Question Number 182947 by myint last updated on 17/Dec/22
$$\mathrm{If}\:\:\mathrm{a}<\:\mathrm{b}<\mathrm{0},\:\:\mathrm{then}\:\:\mid\mathrm{a}−\mathrm{b}\mid\:+\:\mid\mathrm{a}+\mathrm{b}\mid\:+\:\mid\mathrm{ab}\mid= \\ $$
Commented by mr W last updated on 17/Dec/22
$$\neq{constant}\:{value}! \\ $$$${could}\:{be}\:{any}\:{positive}\:{value}! \\ $$
Answered by Frix last updated on 17/Dec/22
$${a}<{b}<\mathrm{0}\:\Rightarrow\:{a}−{b}<\mathrm{0}\wedge{a}+{b}<\mathrm{0}\wedge{ab}>\mathrm{0}\:\Rightarrow \\ $$$$\mid{a}−{b}\mid+\mid{a}+{b}\mid+\mid{ab}\mid= \\ $$$$=−\left({a}−{b}\right)−\left({a}+{b}\right)+{ab}= \\ $$$$=−\mathrm{2}{a}+{ab}={a}\left({b}−\mathrm{2}\right) \\ $$