Mathematics Question from JEE Main 2025 · 7 April, Shift 2

For $t > -1$, let $\alpha_t$ and $\beta_t$ be the roots of the equation

$$\left( (t + 2)^{\frac{1}{7}} - 1 \right)x^2 + \left( (t + 2)^{\frac{1}{6}} - 1 \right)x + \left( (t + 2)^{\frac{1}{21}} - 1 \right) = 0.$$

If $\lim_{t \to -1^+} \alpha_t = a$ and $\lim_{t \to -1^+} \beta_t = b$, then $72(a + b)^2$ is equal to: