Question

Aratati ca urmatoarele numere sunt atat patrate perfecte,cat si cuburi perfecte:
a) t=27·26+27
b) u=27·28-27
c) v=2⁶¹-2⁶⁰
d) w=3³⁷-2·3³⁶
e) s=3¹⁹-3¹⁸-3¹⁸
i) r=(6⁷)⁸:6^2^1

''^'' inseamna la puterea 6 la puterea a 2 la 1

Answer 1

a) t=27·26+27=27(26+1)=27*27= 27²=(3³)²
b) u=27·28-27=27(28-1)=27*27=27²=(3³)²
c) v=2⁶¹-2⁶⁰= 2⁶⁰(2-1)=2⁶⁰=32⁶= (32³)²
d) w=3³⁷-2·3³⁶=3³⁶ (3-2)= 3³⁶= 9¹⁸= (9³)⁶= (729³)²
e) s= 3¹⁹-3¹⁸-3¹⁸= 3¹⁸(3-1-1)= 3¹⁸=(3³)⁶= (27³)²
i) r=(6⁷)⁸:(6²)¹=6⁵⁶:6²= 6⁵⁴= (6⁶)⁹= [(216²)³]³