Question Number 217482 by Rasheed.Sindhi last updated on 14/Mar/25
$$\left(\:{n}\sqrt{\left({n}+\mathrm{1}\right)}\:+\left({n}+\mathrm{1}\right)\sqrt{{n}}\:\:\right)^{{n}} +\left(\:{n}\sqrt{\left({n}+\mathrm{1}\right)}\:−\left({n}+\mathrm{1}\right)\sqrt{{n}}\:\:\right)^{{n}} ={n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right) \\ $$