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x-R-x-1-x-3-x-5-find-the-smallest-value-of-a-given-expression-




Question Number 150486 by mathdanisur last updated on 12/Aug/21
x ∈ R  ∣x - 1∣ + ∣x + 3∣ + ∣x - 5∣  find the smallest value of a given  expression
$$\boldsymbol{\mathrm{x}}\:\in\:\mathbb{R} \\ $$$$\mid\mathrm{x}\:-\:\mathrm{1}\mid\:+\:\mid\mathrm{x}\:+\:\mathrm{3}\mid\:+\:\mid\mathrm{x}\:-\:\mathrm{5}\mid \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{expression} \\ $$
Commented by MJS_new last updated on 12/Aug/21
a, b, c, x ∈ R ∧ a<b<c  min (∣x−a∣+∣x−b∣+∣x−c∣) is at x=b and  its value is c−a  in this case  a=−3∧b=1∧c=5 ⇒ min at x=1 value 8
$${a},\:{b},\:{c},\:{x}\:\in\:\mathbb{R}\:\wedge\:{a}<{b}<{c} \\ $$$$\mathrm{min}\:\left(\mid{x}−{a}\mid+\mid{x}−{b}\mid+\mid{x}−{c}\mid\right)\:\mathrm{is}\:\mathrm{at}\:{x}={b}\:\mathrm{and} \\ $$$$\mathrm{its}\:\mathrm{value}\:\mathrm{is}\:{c}−{a} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{case} \\ $$$${a}=−\mathrm{3}\wedge{b}=\mathrm{1}\wedge{c}=\mathrm{5}\:\Rightarrow\:\mathrm{min}\:\mathrm{at}\:{x}=\mathrm{1}\:\mathrm{value}\:\mathrm{8} \\ $$
Commented by mathdanisur last updated on 13/Aug/21
Thankyou Ser cool
$$\mathrm{Thankyou}\:\mathrm{Ser}\:\mathrm{cool} \\ $$

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