Finding the Maximum Value of (ab + b^2)/(a^2 + b^2): Two Elegant Methods

[@matthewfeig5624]

A trig substitution would work pretty well: a = r*cos t, b = r*sin t for 0

[@chanlyelee]

Thanks for sharing

[@chanlyelee]

Sorry for the following typo errors: 1:33 we consider the quadratic equation (in u), so we shoule write u>0 and u is real. 5:00 equality holds iff (a,b)=((sqrt(2)-1)t ,t) for positive t.

[@gregevgeni1864]

Nice solutions! Thanks for sharing!

[@chanlyelee]

Thanks for watching!

[@makimilanovic76]

Nice, but there's no need to include AI-generated videos of a person. Serves no useful purpose.

[@chanlyelee]

Thanks for the suggestions.