Find the value of 2 2 if 2 and the distance bet... - JAMB Mathematics 2004 Question

\(PQ = \sqrt{(β - 1)^{2} + (1 - α)^{2}}\\ 3 =\sqrt{(β^{2} -2β^{2} + 1 + 1 - 2α + α^{2})}\\ 3 = \sqrt{(α^{2} + β^{2} - 2α + 2β + 2)}\\ 3 = \sqrt{(α^{2} + β^{2} - 2(α + β) + 2)}\\ 3 = \sqrt{(α^{2} + β^{2} - 2 * 2 + 2)}\\ 3 = \sqrt{(α^{2} + β^{2} - 2)}\\ 9 = (α^{2} + β^{2} - 2)\\ α^{2} + β^{2} = 9 + 2\\ α^{2} + β^{2} = 11\)