Question

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Determinati numarul xyz astfel incat xyz, xzy si zyx sunt patrate perfecte.

Answer 1

xyz=100x+10y+z=100xy+z;
⇒xzy=100x+10z+y=100xz+y;
⇒zyx=100z+10y+x=100zy+x;
⇒patratele perfecte de trei cifre sunt
121=11² ,144=12² ,169=13² ,196=14² , 225=15² ,256=16² ,289=17² ,324=18²...961=31²;
⇒xyz=169=13²;
⇒xzy=196=14²;
⇒zyx=961=31²;