Question

What positive number added to its reciprocal gives the minimum sum?

Answer 1

$x+\frac{1}{x}\rightarrow \min \\Cauchy‘s\,\,inequality:\\x+\frac{1}{x}\geqslant 2\sqrt{x\cdot \frac{1}{x}}=2\\The\,\,equality\,holds\,for\,\,x=\frac{1}{x}\Rightarrow x=1\\Answer: 1$