Question

Determină cifrele nenule x si y in baza 10 astfel încât numarul natural a=xxx-xyy+3(y-x)sa fie patrat perfect​

Answer 1

Răspuns:

(x, y)∈{(1;1);(2;2).....(9;9); (3;1) (4;2).....(9;7); (9;1)}

Explicație pas cu pas:

xx-yy+3(y-x)=11(x-y)-3(x-y)=8(x-y), p.p.

x si y , cifre atunci

x-y∈{0;1....9}

x-y=0...8(x-y) =0, p.p....deci x=y si x∈{1;2....9}

x-y=2...8(x-y)=16...p.p. x=3, y=1 x=4,y=2.......x=9, y=7

x-y=8...8(x-y)=64, p.p ...x=9, y=1

(x, y)∈{(1;1);(2;2).....(9;9); (3;1) (4;2).....(9;7); (9;1)}