If $$f(x)=a x^2+b x+c$$ for some $$a, b, c \in R$$ with $$a+b+c=3$$ and $$f(x+y)=f(x)+f(y)+x y, \forall x, y \in R$$. Then, $$\sum_\limits{n=1}^{10} f(n)=$$

The number of positive real roots of the equation $$3^{x+1}+3^{-x+1}=10$$ is

The number of real roots of the equation $$\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}$$ is

If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2+x+1=0$$, then the equation whose roots are $$\alpha^{2021}, \beta^{2021}$$ is given by