Yes, it is possible to win a chess match with only two bishops and one king while the opponent has only one king left. In chess, this is known as a "bishop and king checkmate" or a "smothered mate."
To achieve this, you must use your two bishops and king to force the opponent's king into a corner of the board where it is unable to move, while keeping it under constant attack. Eventually, the opponent's king will be unable to escape and will be checkmated.
Here is an example of how you can achieve this checkmate:
1. Bc4+ Kc5 (or Ke5)
2. Bf1 Kd5
3. Bh3 Kd6
4. Bc8 Kc7
5. Ba6 Kb6
6. Bc4 Kc5
7. Bf7 Kd6
8. Bg8 Ke7
9. Bh7 Kf8
10. Bg6 Kg8
11. Bf5 Kf8
12. Be6 Ke7
13. Bd5 Kd6
14. Bg8 Ke7
15. Bb3 Kf8
16. Ba2 Ke7
17. Bb1 Kd6
18. Bc2 Kc5
19. Bb3 Kb4
20. Bc4 Ka5
21. Kc3 Kb6
22. Kb4 Kc6
23. Bb5+ Kb6 (or Kb7)
24. Bd7 Kc7
25. Bg4 Kd6
26. Kc4 Ke7
27. Kd5 Kf6
28. Kd6 Kg5
29. Kxe5 Kg6
30. Kxf4 Kf6
31. e5+ Ke7
32. Kf5 Kf7
33. e6+ Ke7
34. Ke5 Ke8
35. Kf6 Kf8
36. e7+ Ke8
37. Bh5+ Kd7
38. e8=Q+ Kd6
39. Qe5+ Kc6
40. Bf3+ Kb6
41. Qd5 Ka6
42. Qb3 Ka5
43. Bc6 Ka6
44. Qb5+ Ka7
45. Qb7#
In this example, the two bishops are used to hem in the opponent's king while the king is used to support the bishops and prevent the opponent's king from escaping. Eventually, the opponent's king is forced into a corner and is unable to escape, resulting in a checkmate.
