Find the least value of 3x + 4y if x^2y^3 = 6. I know how to do it by eliminating x and differentiating. But I think there must be a solution using AM (Arithmetic mean) and GM (Geometric mean). What do you think?
What is the value of [math]x[/math] if [math]5 ^ {x + 1} = 6 ^ y[/math] and [math]2 ^ {x + y} = 3 ^ {x - y}[/math]?