The left and right page numbers of an open book are two consecutive integers whose sum is 87.

Left page numbers  are always even  and right page will have a number 1 greater that the left. so  its not possible to have a sum of 87.
If even page  is 2n then right page = 2n + 1:-

2n + 2n + 1 = 87

4n = 86

n = 86 / 4 = 21.5  and 2n = 43  but left page is even  so its not possible to have a sum of left + right = 87.