this is the first time I upload to this site. I got this in my differential and integral mathematics class for physicists:
for $n,m∈\mathbb{N} $ prove:
$$\frac{1}{\sqrt[n]{1+m}}+\frac{1}{\sqrt[m]{1+n}}\ge 1$$
I'm pretty early in the course so I'd preffer a simple answer with use of mainy basic inequalities (the triangle inequality, bernoulis inequality, other simple and basic subjects).