Question

1. Aratati ca urmatoarele numere sunt atat patrate perfecte,cat si cuburi perfecte :
a) t=27*26+27
b) u=27*28-27
c) v=2^61-2^60
2. Aratati ca urmatoarele numere nu sunt patrate perfecte:
a) 14^29+19^29
b) 78^42+42^78

Answer 1

rezolvarea in atasamente

Answer 2

1.

a) t=27*26+27= 27(26+1)=27*27=27²=(3³)²=(3²)³

b) u=27*28-27=27*(28-1)=27*27=27²=(3³)²=(3²)³

c) v=2^61-2^60=2⁶⁰ (2-1)=2⁶⁰= (2³)²⁰= (2³⁰)²


2.
a) 14^29+19^29= 2²⁹* 7 ²⁹+19²⁹
b) 78^42+42^78 =2⁴²*39⁴² +2⁷⁸ *21⁷⁸