Question

Fie nr. nat. nenule de forma xy, yx si zz. Arata ca daca xy+yx=zz,Fie nr. nat. nenule de forma xy, yx si zz. Arata ca daca xy+yx=zz, atunci x+y =zz

Answer 1

x si y clar sunt diferite de 0. Deci, o luam prin incercari.
xy + yx = zz 
zz poate fi 22,33,44,55,66,77,88 sau 99
Daca zz= 22 => x=1,y=1 (11+11= 22)
Daca zz= 33=> x=2 ,y=1 (21+12=33) sau x= 1 si y=2 (12+21=33)
Daca zz=44=> x=1 , y=3 ; sau x=3 , y=1 ; sau x=2 ,y=2
Daca zz=55=> x=1, y=4; sau x=4 si y=1; sau x=2 , y=3;sau x=3 si y=2
Daca zz=66=> x=1,y=5 ; x=5, y=1; x=2 ,y =4 (si invers) ,x=3,y=3
Daca zz=77=>x=1,y=6(si invers) , x=2 ,y=5 (si invers), x=3y=4(si invers)
Daca zz=88=>x=1,y=7(si invers) ; x=2 ,y=6 (si invers), x=3 ,y=5 (si invers), x=4 ,y=4
Daca zz=99=>x=1,y=8 (si invers);x=2,y=7 (si invers) ; x=3, y=6 (si invers) ,x=4, y=5(si invers)