The least positive non-integral solution of the equation $\sin \pi\left(x^2+x\right)=\sin \pi x^2$ is

If $$0< a<5,0< b<5$$ and $$\frac{x^2+5}{2}=x-2[\cos (a+b x)]$$ is satisfied for atleast one real $$x$$, then the least value of $$\frac{a+b}{\pi}$$ is equal to

The roots of the equation $$\cos x+\sqrt{3} \sin x=2 \cos 2 x$$, are