Question

Fie nr nat x=20x5 la puterea 2015x2 la puterea 2014-2017
Aratati ca x+2017 este patrat perfect si cub perfect

Answer 1

x = 20 x 5^2015 x 2^2014 - 2017 = 20 x 5 x 5^2014 x 2^2014 - 2017 = 100 x (5x2)^2014 - 2017 = 10^2 x 10^2014 - 2017 = 10^2016 - 2017

x + 2017 = 10^2016 - 2017 + 2017 = 10^2016 = (10^1008)^2 = (10^672)^3, deci este si patrat perfect, si cub perfect