Explicație pas cu pas:
[tex] \frac{x}{ \sqrt{2} } + \frac{y}{ \sqrt{3} } = \sqrt{ \frac{5}{6} } \\ \frac{x}{ \sqrt{3} } + \frac{y}{ \sqrt{2} } = \sqrt{ \frac{5}{6} } \\ \\ x \sqrt{3} + y \sqrt{2} = \sqrt{5} \\ x \sqrt{2} + y \sqrt{3} = \sqrt{5} \\ \\ - x \sqrt{6 } - 2y = - \sqrt{10} \\ x \sqrt{6} + 3y = \sqrt{15} \\ \\ y = \sqrt{15} - \sqrt{10} \\ y= \sqrt{5} ( \sqrt{3} - \sqrt{2} ) \\ \\ x \sqrt{3} + \sqrt{5} ( \sqrt{3} - \sqrt{2} ) \sqrt{2} = \sqrt{5} \\ x \sqrt{3} + \sqrt{5} ( \sqrt{6}-2) = \sqrt{5} \\ x \sqrt{3} = \sqrt{5} (1 - \sqrt{6} + 2) \\ x = \frac{\sqrt{5} (3 - \sqrt{6})}{ \sqrt{3} } = \frac{\sqrt{5} (3 \sqrt{3} - 3\sqrt{2})}{3} \\ x = \sqrt{5} (\sqrt{3} - \sqrt{2})[/tex]
