Limits Continuity And Differentiability

For $\mathrm{t}>-1$, let $\alpha_{\mathrm{t}}$ and $\beta_{\mathrm{t}}$ be the roots of the equation

\(\left((\mathrm{t}+2)^{1 / 7}-1\right) x^2+\left((\mathrm{t}+2)^{1 / 6}-1\right) x+\left((\mathrm{t}+2)^{1 / 21}-1\right)=0 \text {. If } \lim \limits_{\mathrm{t} \rightarrow-1^{+}} \alpha_{\mathrm{t}}=\mathrm{a} \text { and } \lim \limits_{\mathrm{t} \rightarrow-1^{+}} \beta_{\mathrm{t}}=\mathrm{b} \text {, }\)

then $72(a+b)^2$ is equal to ___________.