For what value of ‘ p’ is x + ¼ √x+p2 is perfect square

For what value of ‘ p’ is x + ¼ √x+p2 is perfect square.
(a) -1/8
(b) 1/8
(c) 1/12
(d) -1/12
Sol:

For what value of ‘ p’ is x + ¼ √x+p2 is perfect square.
(a) -1/8
(b) 1/8
(c) 1/12
(d) -1/12
Sol: