The Process of Decision Making in Chess Volume 2: Practice positions and solutions. Position 9.5

Solve for white:

Diagram 9.5- white has an isolated pawn which is also blockaded from advancing. Generally this means that the weakness becomes long-lasting or even permanent. Going through threats analysis, white noticed that although the d4 pawn is attacked twice and defended twice, it can still be captured: …Nxd4, Bxd4 …Rxd4! And black’s rook is immune on d4 due to the mating threat Re1. If white could only get rid of this weak pawn, possibly by pushing it… But sadly the pawn is indeed blockaded, and white’s fantasy cannot come true in the given position.

Challenge: if getting rid of the weakness is impossible, is there a solution to the threat we found that doesn’t involve concessions?

I don't want to give the answer away (the rest of the response is written in white - and can highlight over the next part if you want to see it), but it sounds like we need to connect the rooks.  Ba2 sounds like a good plan.  The pawn on a is still protected by the knight and queen.  The rook has more important plans.

Could you not accomplish the same by Ne2? I accept your solution is better but I am not sure why.

I looked at Ne2, but I am one not to move my knights backwards.   With the knight on c3, it is stopping the queen from wrecking havoc on the 1st rank and the knight is still controlling (although not as well as black) the d5 square.

Ne2 makes e1 square weak to the black queen so d pawn is sadly lost agian

Qd3 seems like to not lose any matireal as i see and it do not make any concession as I see

After puzzling this for a while, I think the solution is correct not because it alleviates the weakness of d4, but because it develops the bishop and connects the rooks.  The weakness of the e2 square from Ne2 would take some time to exploit, if it could be exploited (several moves available to support e2).

ne2 then the d4 pawn falls does it not?

The tactic works because the rook on d1 is protecting both the d4 pawn and the back rank—in other words, it's overloaded. Also, our bishop on b1 isn't really accomplishing anything. Ba2 both connects the rooks (thereby unoverloading the rook on d1), and brings white's light-squared bishop into the game, by pressuring black's active knight on e6. Other options for eliminating the back rank mate tactic included moving one of the pawns in front of the king, but these solutions seem inferior since they don't address as many of the requirements of the position.

@moonmaster9000 nice find dude

thank you @glenni3377!