Question Number 33363 by soufiane zarik last updated on 15/Apr/18
Commented by soufiane zarik last updated on 15/Apr/18
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:!! \\ $$
Commented by Rasheed.Sindhi last updated on 15/Apr/18
$$\mathrm{If}\:\:\:\mathrm{m},\mathrm{n}\in\mathbb{Z} \\ $$$$\sqrt{\mathrm{m}}+\sqrt{\mathrm{n}}=\mathrm{2}\sqrt{\mathrm{3}} \\ $$$$\sqrt{\mathrm{m}}+\sqrt{\mathrm{n}}=\sqrt{\mathrm{3}}+\sqrt{\mathrm{3}} \\ $$$$\mathrm{m}=\mathrm{n}=\mathrm{3} \\ $$$$\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} =\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} =\mathrm{18} \\ $$
Commented by MJS last updated on 15/Apr/18
$${m},\:{n}\in\mathbb{Z} \\ $$$${m}=\mathrm{0}\:\Rightarrow\:{n}=\mathrm{12}\:\Rightarrow\:{m}^{\mathrm{2}} +{n}^{\mathrm{2}} =\mathrm{144} \\ $$