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How Does a Constant Product Formula (X Y=k) Govern the Price in a DEX Smart Contract?

The constant product formula ensures that the product of the quantities of two assets (x and y) in a liquidity pool remains constant (k). When a user buys asset x, they reduce x and increase y.

To maintain k, the contract logic requires the user to deposit more y than they withdrew x, thus increasing the price of x relative to y. This formula algorithmically determines the exchange rate and provides continuous liquidity.

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