SEAMO 2023 — Paper E — Grade 9–10 Question 11

For positive real numbers $a,b,c$, find the minimum of $u=\left\lfloor\dfrac{a+b}{c}\right\rfloor+\left\lfloor\dfrac{b+c}{a}\right\rfloor+\left\lfloor\dfrac{c+a}{b}\right\rfloor$, where the brackets denote the integer part.