Let $\alpha, \beta, \gamma$ and $\delta$ be the coefficients of $x^7, x^5, x^3$ and $x$ respectively in the expansion of $\left(x+\sqrt{x^3-1}\right)^5+\left(x-\sqrt{x^3-1}\right)^5, x1$. 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 : [JEE Main 2025, 22 Jan (Shift 2)]

Question

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 : [JEE Main 2025, 22 Jan (Shift 2)]

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Let \(\alpha, \beta, \gamma\) and \(\delta\) be the coefficients of \(x^7, x^5, x^3\) and \(x\) respectively in the expa…

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