Question 189204
Question #1:
Let x, x+1, x+2 = 3 consecutive integers

{{{x^2+(x+1)^2=(x+2)^2}}}

{{{x^2+x^2+2x+1=x^2+4x+4}}}

{{{2x^2+2x+1=x^2+4x+4}}}

{{{2x^2-x^2+2x-4x+1-4=0}}}

{{{x^2-2x-3=0}}}

{{{(x-3)(x+1)=0}}}

x-3=0       x+1=0
x=3         x=-1

The possible answers are:
3,4,5  or -1,0,1

Question #2:
Let x, x+2, x+4 = consecutive odd numbers

{{{x+(x+2)+(x+4)=x*(x+2)-36}}}

{{{3x+6=x^2+2x-36}}}

{{{x^2-x-42=0}}}

{{{(x-7)(x+6)=0}}}

x-7=0    x+6=0

x=7   or x=-6

Since we are looking for odd numbers, the correct answer should be
7,9,11