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Limits Continuity and Differentiability question

2025 · 7 Apr · Shift 2 · Q50

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 7 Apr · Shift 2 · Q50

Limits Continuity and Differentiability question

2025 · 7 Apr · Shift 2 · Q50

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

For

\mathrm{t}\gt -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

\underline{\hspace{2cm}}

.

Numerical answer

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