Mathematics

Mathematics

Problem

Let P(−2,−1,1)P(-2, -1, 1) and Q(5617,4317,11117)Q\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right) be the vertices of the rhombus PRQSPRQS. If the direction ratios of the diagonal RSRS are α,−1,β\alpha, -1, \beta, where both α\alpha and β\beta are integers of minimum absolute values, then α2+β2\alpha^2 + \beta^2 is equal to _____.

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