Let f be a differentiable function satisfying f(x)=2/(√ 3) ∫_0^√ 3 f((λ^2 x)/3) d λ, x>0 and f(1)=√ 3. If y=f(x) passes through the point (α, 6),…

Let $\displaystyle f$ be a differentiable function satisfying $\displaystyle f(x)=\frac{2}{\sqrt{3}} \int_0^{\sqrt{3}} f\left(\frac{\lambda^2 x}{3}\right) \mathrm{d} \lambda, x>0$ and $\displaystyle f(1)=\sqrt{3}$. If $\displaystyle y=f(x)$ passes through the point $\displaystyle (\alpha, 6)$, then $\displaystyle \alpha$ is equal to \_\_\_\_.