Let α, β, γ and δ be the coefficients of x⁷, x⁵, x³ and x respectively in the expansion of (x+√(x³-1))⁵+(x-√(x³-1))⁵, x>1. If u and v satisfy the equations α u+β v = 18 γ u+δ v = 20 then u+v equals:

Binomial Theorem and Its Simple Applications: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q28

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let

\alpha, \beta, \gamma

and

\delta

be the coefficients of

x^7, x^5, x^3

and

x

respectively in the expansion of

\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5, x>1

. If

u

and

v

satisfy the equations

\begin{aligned} \alpha u+\beta v &= 18 \\ \gamma u+\delta v &= 20 \end{aligned}

then

u+v

equals: