Question Number 1734 by Rasheed Ahmad last updated on 07/Sep/15
$$\boldsymbol{\mathrm{a}}\:\:{belongs}\:{to}\:{an}\:{interval}\:\boldsymbol{\mathrm{A}}\:{and} \\ $$$$\boldsymbol{\mathrm{k}}\in\mathbb{R}^{+} \:\:{is}\:{a}\:{constant}.\:{Determine} \\ $$$$\boldsymbol{\mathrm{A}}\:{in}\:{case} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mid\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{k}}\mid^{\mid\:\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{k}}\:\mid} \geqslant\:\mid\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{k}}\mid^{\mid\boldsymbol{\mathrm{a}}−\boldsymbol{\mathrm{k}}\mid} \: \\ $$$$ \\ $$