Question

Aratati ca urmatoarele numere sunt patrate perfecte
2la83-4la41 =
11ori (5la21-5la20-5la18)=

Answer 1

[tex]2^{83}-4^{41}=2^{83}-(2^2)^{41}=2^{83}-2^{82}=2^{82}(2-1)=2^{82} \\2^{82}=(2^{41})^2\text{ deci este patrat perfect} \\ 11(5^{21}-5^{20}-5^{18})=11\cdot5^{18}(5^3-5^2-1)=5^{18}\cdot11\cdot99\\ =5^{18}\cdot9\cdot11^2=(5^9\cdot3\cdot11)^2 \text{ care este patrat perfect }[/tex]