Question

Aratati ca numerele x si y sunt patrate perfecte,daca:
x=[2 la puterea 30 la puterea 2•2+(64 la puterea 4)la puterea 100:2 la 899] totul la 2+ la 3007; y=5•(3 la 2002-3 la 2001-9 la 1000).

Answer 1

x=[2⁶⁰·2+64⁴⁰⁰:2⁸⁹⁹]²+
x=[2⁶⁰⁺¹+(2⁶)⁴⁰⁰:2⁸⁹⁹]²+
x=(2⁶¹+2²⁴⁰⁰:2⁸⁹⁹)²+
x=(2⁶¹+2²⁴⁰⁰⁻⁸⁹⁹)²+
x=(2⁶¹+2¹⁵⁰¹)²+

y=5·(3²⁰⁰²-3²⁰⁰¹-(3²)¹⁰⁰⁰)
y=5·(3²⁰⁰²-3²⁰⁰¹-3²⁰⁰⁰)
y=5·3²⁰⁰⁰(3²-3-1)
y=5·3²⁰⁰⁰·5
y=5¹⁺¹·3²⁰⁰⁰
y=5²·(3¹⁰⁰⁰)² este patrat perfect