# Cool Inequality #1 Only AM-GM

Algebra Level 4

$\frac{a}{b} \ge 3x^{3}y(12-7xy-3x^{2})$

If $$x,y>0$$ and $$a>6,b>1$$ and above inequality is satisfied for some co-prime integers $$a$$ and $$b$$. Find $$a+b$$.

Note:- Use only AM-GM to find the answer.

×