Bankers Algorithm-Is the system in safe state?
you can say there is no deadlock if there is a safe sequence for the completion, after $P1$ request is granted there must be a safe sequence where by which every process is completed.

After P1 request is granted
                      |   P1  |  P2  |   P3   |
Max Requirement       |   8   |  7   |   5    |
Current Allocation    |   4   |  1   |   3    |
Balance Requirement   |   4   |  6   |   2    |
now the resources left over are 10-4-1-3=2


so can we complete with 2 resources? any sequence is possible?

YES

if P3 is given 2 resources it will complete and release all the current allocated resources so our resource count becomes 5 , now we have 5 and we can complete P1 and get back 4 now our resource count is 9 and i need just 6 to complete P2 so a safe sequence is possible.
so safe sequence will be 

$P3 \rightarrow P1\rightarrow P2$ 

so $P1$ request is granted