Answer:
possible integers are 3, -3 , 4 and -4
Step-by-step explanation:
Let the consecutive positive integers be x and x+1
[tex]x^{2} +(x+1)^{2} = 25 \\x^{2} +(x^{2} +2x +1)=25\\[/tex]
[tex]2x^{2} + 2x -24 =0[/tex]
[tex]x^{2} + x - 12 = 0[/tex]
(x+4)(x-3) = 0
x = -4, 3
x+1 = -3, 4
