Let α, β be the roots of the equation x² - ax - b = 0 with Im(α) < Im(β). Let P n = αⁿ - βⁿ. If P₃ = -5√(7)i, P₄ = -3√(7)i, P₅ = 11√(7)i and P₆ = 45√(7)i, then |α⁴ + β⁴| is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q250

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

Let

\alpha, \beta

be the roots of the equation

x^2 - ax - b = 0

with

\operatorname{Im}(\alpha) < \operatorname{Im}(\beta)

. Let

P_n = \alpha^n - \beta^n

. If

\mathbf{P}_3 = -5\sqrt{7}i

\mathbf{P}_4 = -3\sqrt{7}i

\mathbf{P}_5 = 11\sqrt{7}i

and

\mathbf{P}_6 = 45\sqrt{7}i

, then

|\alpha^4 + \beta^4|

is equal to:

Your answerInteger or decimal