Let A B C be an isosceles triangle in which A is at (-1,0), ∠ A=(2 π)/3, A B=A C and B is on the positve x -axis. If B C=4 √ 3 and the line B C…

Let $\displaystyle A B C$ be an isosceles triangle in which $\displaystyle A$ is at $\displaystyle (-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $\displaystyle B$ is on the positve $\displaystyle x$-axis. If $\displaystyle B C=4 \sqrt{3}$ and the line $\displaystyle B C$ intersects the line $\displaystyle y=x+3$ at $\displaystyle (\alpha, \beta)$, then $\displaystyle \frac{\beta^4}{\alpha^2}$ is $\displaystyle \_\_\_\_$.