How Does the Constant Product Formula (X Y=k) Directly Give Rise to the Impermanent Loss Phenomenon?

The constant product formula (x y=k) forces the total value of the reserves (k) to remain constant. When an external market price of asset 'x' increases, arbitrageurs buy 'x' from the pool at a lower price and sell 'y' to it.

This rebalances the pool to match the new external price, leaving the liquidity provider with less of the appreciated asset 'x' and more of the depreciated asset 'y'. Impermanent loss is the value difference between this new asset mix and the mix they would have had by just holding.