IB Maths AA HL Sl 1 1 Scientific Notation Topic Practice

In this question, you will investigate the maximum product of positive real numbers with a given sum.
Consider the two numbers $x_{1}, x_{2} \in \mathbb{R}^{+}$, such that $x_{1}+x_{2}=12$.

Use your answer to part (h) to find the largest possible product of positive numbers whose sum is 100 . Give your answer in the form $a \times 10^{k}$, where $1 \leq a<10$ and $k \in \mathbb{Z}^{+}$.