Inequality of The Day

For $a,b,x,y$ real numbers, prove that:

$(3a^2+2ab+5b^2)(3x^2 + 2xy + 5y^2) \geq (3ax + ay + bx + 5by)^2$

Generalization: for $a,b,x,y$ real numbers, and $P,Q,R$ real numbers such that $Q^2 < PR$, prove that:

$(Pa^2+2Qab+Rb^2)(Px^2 + 2Qxy + Ry^2) \geq (Pax + Qay + Qbx + Rby)^2$