Let α, β be the roots of the equation x^2-4 λ x+5=0 and α, γ be the roots of the equation x^2-(3 √ 2 +2 √ 3 ) x+7+3 λ √ 3 =0, λ>0. If β+γ=3 √ 2, then…

Let $\displaystyle \alpha, \beta$ be the roots of the equation $\displaystyle x^2-4 \lambda x+5=0$ and $\displaystyle \alpha, \gamma$ be the roots of the equation $\displaystyle x^2-(3 \sqrt{2}+2 \sqrt{3}) x+7+3 \lambda \sqrt{3}=0, \lambda>0$. If $\displaystyle \beta+\gamma=3 \sqrt{2}$, then $\displaystyle (\alpha+2 \beta+\gamma)^2$ is equal to \_\_\_\_.