Question

Aratati Ca numarul x si y sunt patrate perfecte daca x=[2^30^2×(2^6)^100×2+(64^4)^100÷2^899]^2+2^3007
y=5×(3^2002-3^2001-9^1000)​

Answer 1

Răspuns:

x=[2³⁰^²x(2⁶)¹⁰⁰ˣ2+(64⁴)¹⁰⁰:2⁸⁹⁹]²2+2³⁰⁰⁷

=(2⁹⁰⁰·2⁶⁰⁰·2+2²⁴⁰⁰:2⁸⁹⁹)²+2³⁰⁰⁷

=(2¹⁵⁰¹+2¹⁵⁰¹)²+2³⁰⁰⁷

=(2·2¹⁵⁰¹)²+2³⁰⁰⁷

=2¹⁵⁰²ˣ²+2³⁰⁰⁷

=2³⁰⁰⁴+2³⁰⁰⁷=2³⁰⁰⁴(1+2³)=2³⁰⁰⁴·9=2¹⁵⁰²ˣ²·3²=(2¹⁵⁰²·3)² este pp

y=5*(3²⁰⁰²-3²⁰⁰¹-9¹⁰⁰⁰)

=5·(3²⁰⁰²-3²⁰⁰¹-3²⁰⁰⁰)

=5·3²⁰⁰⁰(3²-3-1)

=5·3²⁰⁰⁰·5=5²·3¹⁰⁰⁰ˣ²=(5·3¹⁰⁰⁰)² este pp