BESTWAY 14 Arătaţi că numerele x şi y sunt pătrate perfecte: x=[230 (26) 100 2+(64¹) 100: 2899] 3007 +230 şi y = 5(32002- 32001 - 91000). Rezolvare: X = [2³0² (26)¹00.2+(64³) √2 ·(251¹00 2+(65³) ¹00: 289972 +2³ 300 3007 300€ 2 p.p => 2 р.р

Răspuns:
Explicație pas cu pas:
x=[2⁽³⁰⁾⁽²⁾·(2⁶)¹⁰⁰·2+(64⁴)¹⁰⁰:2⁸⁹⁹]²+2³⁰⁰⁷ =
[2⁹⁰⁰·2⁽⁶ˣ¹⁰⁰⁾·2+64⁽⁴ˣ¹⁰⁰⁾:2⁸⁹⁹]²+2³⁰⁰⁷=
[2⁹⁰⁰·2⁶⁰⁰·2+64⁴⁰⁰:2⁸⁹⁹]²+2³⁰⁰⁷=[2⁽⁹⁰⁰⁺⁶⁰⁰⁺¹⁾+(2⁶)⁴⁰⁰:2⁸⁹⁹]²+2³⁰⁰⁷=
[2¹⁵⁰¹+2⁽⁶ˣ⁴⁰⁰⁾:2⁸⁹⁹]²+2³⁰⁰⁷=[2¹⁵⁰¹+2²⁴⁰⁰:2⁸⁹⁹]²+2³⁰⁰⁷=[2¹⁵⁰¹+2⁽²⁴⁰⁰⁻⁸⁹⁹⁾]²+2³⁰⁰⁷=
[2¹⁵⁰¹+2¹⁵⁰¹]²+2¹³⁰⁷=[2¹⁵⁰¹·2]²+2³⁰⁰⁷==[2⁽¹⁵⁰¹⁺¹⁾]²+2³⁰⁰⁷=[2¹⁵⁰²]²+2³⁰⁰⁷=
2⁽¹⁵⁰²ˣ²⁾+2³⁰⁰⁷=2³⁰⁰⁴+2³⁰⁰⁷=2³⁰⁰⁴·(1+2³)=2³⁰⁰⁴·(1+8)=2³⁰⁰⁴·9=2³⁰⁰⁴·3²=(2¹⁵⁰²)²·3²=(2¹⁵⁰²·3)²
y=5·(3²⁰⁰²-3²⁰⁰¹-9¹⁰⁰⁰)=5·[3²⁰⁰²-3²⁰⁰¹-(3²)¹⁰⁰⁰]=5·[3²⁰⁰²-3²⁰⁰¹-3⁽²ˣ¹⁰⁰⁰⁾]=
5·(3²⁰⁰²-3²⁰⁰¹-3²⁰⁰⁰)=5·3²⁰⁰⁰·(3²-3¹-1)=5·3²⁰⁰⁰·(9-3-1)=5·3²⁰⁰⁰·5=5²·3²⁰⁰⁰=
5²·(3¹⁰⁰⁰)²=(5·3¹⁰⁰⁰)²