Use the AM-GM inequality to prove $(5xy + 6y)^3$ ≥ $1215xy^3$ for all real numbers $x, y > 0.$
Not sure if I was on the right track but so for my understanding is:
since there is a power of 3 on the left we need 3 numbers
so you have $5xy + 3y + 3y$ ≥ $3(5x \times 3y \times 3y)^3$
bit stuck after this, or am I completely on the wrong track?
$5xy+3y+3y \geq 3(5xy*3y*3y)^{1/3}$ now if you raise both sides to the power 3 we get the result.