Question

Calculati suma tuturor numerelor xy ,stiind ca xy=4x+3y.

Answer 1

xy-numar natural;
⇒xy=10x+y;
⇒xy=4x+3y;
⇒10x+y=4x+3y
⇒10x-4x=3y-y⇒6x=2y⇒3x=y⇒y-cifra naturala;
⇒y∈[3,6,9]⇒multiplu de 3 [ca si cifra];
⇒x∈[1,2,3];
⇒numerele gasite sunt:13,26,39;
⇒13+26+39=39+39=39·2=78⇒suma tuturor numerelor care respecta cerinta;