Question

Sa se determine perechile de cifre(x si y)pentru care 3x+4y este patrat perfect

Answer 1

3x+4y=3x+3y+y=3(x+y)+y
3x+4y=4x-x+4y=4(x+y)-x

Deci (3x+4y)=$M_{3}+y= \frac{M}{4}-x$

Numerele de forma $M_{3},~ M_{4}+2 ~si~ M_{4}+3 ~nu~pot~fi~patrate~perfecte =>$ x∉{1,2,5,6,9} si y∉{2,5,8}.
Deci x∈{0,3,4,7,8}.

x=0 => y∈{0,1,4,9}
x=3 => y∈{0,4}
x=4 => y∈{1,6}
x=7 => y∈{1,7}
x=8 => y=3.

(x,y)∈{(0,0);(0,1);(0,4);(0,9);(3,0);(3,4);(4,1);(4,6);(7,1);(7,7);(8,3)}.