Răspuns:
A= 2017+2×2016×2017:2 (am aplicat formula Gauss)
A=2017+2016×2017
A=2017×(1+2016)
A=2017×2017
A=2017² --> este pătrat perfect
B=1+3+5+....+2017 (am aplicat formula Gauss)
B=1+2+3+4+....+2017 -(2+4+6+....+2016)
B=2017×2018 : 2 - 2×(1+2+3+.....1008)
B=2017×1009 - 2×1008×1009:2
B=2017×1009-1008×1009
B=1009×(2017-1008)
B=1009×1009
B=1009² --> este pătrat perfect
C=81+81×2+81×3+....+49×81 (dam factor comun)
C=81×(1+2+3+....+49)
C=81×49×50:2
C=81×49×25
C=9²×7²×5² (scriem numerele ca pătrate perfecte)
C=(9×7×5)² --> este pătrat perfect
D=2×(1+2+3+...+124)+125
D=2×124×125 : 2+125
D=124×125+125
D=125×(124+1)
D=125×125
D=5³×5³
D=(5×5)³ --> este cub perfect
Sper ca te-am ajutat! Succes la teme!
