x: menor numero ; y: mayor numero ; y=x+1
[tex]x^{2} + (y)^{2} = (y) + 10(x+y) [/tex]
[tex]x^{2} + (x+1)^{2} = (x+1) + 10((x)+(x+1)) [/tex]
[tex]x^{2}+x^{2}+2x+1=x+1+10(2x+1)[/tex]
[tex]2x^{2}+2x+1=x+1+20x+10[/tex]
[tex]2x^{2}+2x+1=21x+11[/tex]
[tex]x^{2}+2x+1-21x-11=0[/tex]
[tex]x^{2}-19x-10=0[/tex] ; por aspa simple
[tex](2x+1)(x-10)=0[/tex]
sacamos que
x={-1/2; + 10} ; x pertenece a los enteros
entonces x=10
respuesta: 10 y 11