Let α and β be two real roots of the equation ( k +1) tan^2 x-√ 2 · λ tan x=(1- k ), where k (≠-1) and λ are real numbers. If tan^2(α+β)=50, then a…

Let $\displaystyle \alpha$ and $\displaystyle \beta$ be two real roots of the equation $\displaystyle (\mathrm{k}+1) \tan ^2 x-\sqrt{2} \cdot \lambda \tan x=(1-\mathrm{k})$, where $\displaystyle \mathrm{k}(\neq-1)$ and $\displaystyle \lambda$ are real numbers. If $\displaystyle \tan ^2(\alpha+\beta)=50$, then a value of $\displaystyle \lambda$ is :