Let x = 1st positive integer
Let x + 1 = 2nd positive integer
As give, their sum of squares is 841
[tex]x^{2}+(x+1)^{2}=841[/tex]
[tex]x^{2}+x^{2}+2x+1=841[/tex]
[tex]2x^{2}+2x+1=841[/tex]
[tex]2x^{2}+2x-840=0[/tex]
factor 2 out, [tex]x^{2}+x-420=0[/tex]
[tex]x^{2}+21x-20x-420=0[/tex]
[tex]x(x+21)-20(x+21)=0[/tex]
(x+21)(x-20)
This gives, x=20 and =-21 (neglect the negative value)
So, x = 20
x+1 = 21
So, the two numbers are : 20 and 21
