Question Number 79289 by 21042009 last updated on 24/Jan/20
$${m}^{\mathrm{2}} +{n}^{\mathrm{2}} =\mathrm{2}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$$${What}\:{is}\:\mathrm{2}\left({a}+{b}\right)\:{in}\:{terms}\:{of}\:{m}\:{and}\:{n} \\ $$
Commented by mr W last updated on 24/Jan/20
$${a}+{b}=\pm\sqrt{\left({a}+{b}\right)^{\mathrm{2}} }=\pm\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{2}{ab}} \\ $$$$=\pm\sqrt{\frac{{m}^{\mathrm{2}} +{n}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{2}{ab}} \\ $$$${that}\:{means}\:{you}\:{can}\:{not}\:{determine} \\ $$$$\mathrm{2}\left({a}+{b}\right)\:{only}\:{in}\:{terms}\:{of}\:{m}\:{and}\:{n}! \\ $$