Impact of French society: towns such as Chartres are becoming "TGV commuter belt"; Brussels - Paris in 90 minutes has increased commuting between the two capitals; likewise Paris - Marseille time greatly reduced recently
Impact of the building of the lines: many years of wrangles over the Lyon-Marseille line
... will make it a perfect square trinomial of the form x2 + 2xy + y2. Since "2xy" in this case is (b/a)x, we must have y = b/(2a), so we add the square of b/(2a) to both ...