For t > -1, let α t and β t be the roots of the equation ((t + 2)^(1/7) - 1)x² + ((t + 2)^(1/6) - 1)x + ((t + 2)^(1/21) - 1) = 0. If lim t → -1⁺ α t = a and lim t → -1⁺ β t = b, then 72(a + b)² is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q173

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

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.

\lim_{t \to -1^+} \alpha_t = a

and

\lim_{t \to -1^+} \beta_t = b

, then

72(a + b)^2

is equal to:

Your answerInteger or decimal