What’s The Difference Between Max and Min?

🎯 Math Games | Solution 6 | 17/6/2024

I think this week’s challenge is slightly easier than previous rounds. Either way, another round of applause to this week’s winners 👏👏👏

1st Place: Alfredo Esposito 7 Points 🥇

2nd Place: Neil Faver 5 Points 🥈

3rd Place: Wotsit 3 Points 🥉

Other Challengers: Aaron Tovish, Jonathan Lynn Harvey 1 Point each 🎯

Here’s the solution 👑

Solution

We can first rearrange the two equations and put all as and bs to one side

The trick to this question is to take a leap of faith and let x be an arbitrary variable

This inequality is true because we are adding up two square terms and every square term must be greater than or equal to zero.

If we expand the terms, we get the following quadratic inequality

Notice the terms (a + b) and (a² + b²) can be written in terms of c