Using momentum conservation
$\vec{P}=\vec{P}_{1}+\vec{P}_{2}=\frac{h}{\lambda_{1}} \hat{i}+\frac{h}{\lambda_{2}} \hat{j}$
$|\vec P| = \sqrt {{{\left( {\frac{h}{{{\lambda _1}}}} \right)}^2} + {{\left( {\frac{h}{{{\lambda _2}}}} \right)}^2}} $
$\frac{h}{\lambda}=\sqrt{\left(\frac{h}{\lambda_{1}}\right)^{2}+\left(\frac{h}{\lambda_{2}}\right)^{2}}$
$\frac{1}{\lambda^{2}}=\frac{1}{\lambda_{1}^{2}}+\frac{1}{\lambda_{2}^{2}}$
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