Question Number 183935 by SulaymonNorboyev last updated on 31/Dec/22
$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}={A} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}=? \\ $$
Answered by Rasheed.Sindhi last updated on 31/Dec/22
$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}={A}\: \\ $$$$\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}=? \\ $$$$\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\right)\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={A}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\right) \\ $$$$\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\right)=\frac{\mathrm{1}}{{A}}\left\{\left({x}^{\mathrm{2}} +\mathrm{2}\right)−\left({x}^{\mathrm{2}} −\mathrm{4}\right)\right\} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:=\frac{\mathrm{6}}{{A}} \\ $$
Commented by SulaymonNorboyev last updated on 31/Dec/22
$$ \\ $$$${THANKS}\:{YOU} \\ $$
Answered by Rasheed.Sindhi last updated on 31/Dec/22
$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}={A} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}=? \\ $$$${a}=\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\:,\:{b}=\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\: \\ $$$${a}+{b}={A}………\left({i}\right) \\ $$$${a}^{\mathrm{2}} −{b}^{\mathrm{2}} =\left({x}^{\mathrm{2}} +\mathrm{2}\right)−\left({x}^{\mathrm{2}} −\mathrm{4}\right)=\mathrm{6} \\ $$$${a}−{b}=\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{{a}+{b}}=\frac{\mathrm{6}}{{A}} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{6}}{{A}} \\ $$
Answered by manolex last updated on 31/Dec/22
$${m}+{n}={A}\:\:\:\:\:\:{find}\:\:\:{m}−{n} \\ $$$$\left({m}+{n}\right)\left({m}−{n}\right)=\left({m}−{n}\right){A} \\ $$$${x}^{\mathrm{2}} +\mathrm{2}−{x}^{\mathrm{2}} +\mathrm{4}=\left({m}−{n}\right){A} \\ $$$$\frac{\mathrm{6}}{{A}}=\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}\:\:\:\:\:\:{is}\:{answer} \\ $$