SEAMO X 2023 — Paper E — Grade 9–10 Question 14

Let $[a]$ denote the integer part and $\{a\}$ the fractional part; for example $[6.5]=6$, $\{6.5\}=0.5$. The positive solution of $[x]^2=\{x\}x$ is $x=(a+\sqrt b)/2$. Find $a+b$.