For these reasons Black has no choice but has to play (2) …, Pxd4. True enough, Black gives up his center-Pawn with this exchange, but White cannot prevent P-d5 in the long run, so that he also loses his center-Pawn and has no advantage over Black in that respect. The following variations are typical for the line of play in cases of this kind. White tries to hold back Black's Queen's Pawn as long as he can, but finally Black enforces the advance.
I. (3) Qxd4 Kt-c6 (4) Q-e3
Now P-d5 is not possible because of Pxd5 check.
(4) … Kt-f6 (5) Kt-c3 B-e7 (6) B-d2 P-d5
Threatening to win a piece by P-d4.
(7) Pxd5 Ktxd5
Now White has no center-Pawn either; Black has a perfectly good game.
II. (3) Kt-f3 Kt-c6
Most players would be tempted to play P-c5 instead. But this must be bad as it is a Pawn move which is not necessary. Black does not need to defend the Pawn d4 as he is a Pawn ahead; and the development of the pieces is much more valuable than the advantage of a Pawn. White would obtain a far superior position with (4) P-c3, Pxc3; (5) Ktxc3, after which Black cannot hope ever to free his game by P-d5.
(4) Ktxd4 Kt-f6