Question

Aratati ca numerele x si y sunt patrate perfecte:
[tex]x=[ 2^{30^2}* (2^6) ^{100}*2+(64^4)^{100}:2^{899}]^2+2^{3007} si
,[/tex] $y=5*( 3^{2002}- 3^{2001}-9^{1000})$

Answer 1

x=[2⁹⁰⁰*2⁶⁰⁰*2+2²⁴⁰⁰:2⁸⁹⁹]²+2³⁰⁰⁷=
  =(2¹⁵⁰¹+2¹⁵⁰¹)²+2³⁰⁰⁷=(2¹⁵⁰²)²+2³⁰⁰⁷=2³⁰⁰⁴+2³⁰⁰⁷=2³⁰⁰⁴*(1+2³)=(2¹⁵⁰²)² * 3² =p.p. ;

y=5*(3²⁰⁰²-3²⁰⁰¹-3²⁰⁰⁰)=5*3²⁰⁰⁰ * (3² - 3 -1)=(3¹⁰⁰⁰)² * 5² = p.p. ;