For t >-1, let α_t and β_t be the roots of the equation (( t +2)^1 / 7-1) x^2+(( t +2)^1 / 6-1) x+(( t +2)^1 / 21-1)=0. If lim_t →-1^+ α_t = a and…

For $\displaystyle \mathrm{t}>-1$, let $\displaystyle \alpha_{\mathrm{t}}$ and $\displaystyle \beta_{\mathrm{t}}$ be the roots of the equation $\displaystyle \left((\mathrm{t}+2)^{1 / 7}-1\right) x^2+\left((\mathrm{t}+2)^{1 / 6}-1\right) x+\left((\mathrm{t}+2)^{1 / 21}-1\right)=0$. If $\displaystyle \lim _{\mathrm{t} \rightarrow-1^{+}} \alpha_{\mathrm{t}}=\mathrm{a}$ and $\displaystyle \lim _{\mathrm{t} \rightarrow-1^{+}} \beta_{\mathrm{t}}=\mathrm{b}$, then $\displaystyle 72(a+b)^2$ is equal to $\displaystyle \_\_\_\_$.