Question

demonstati ca este patrat perfecr 11*(5 la puterea a 21 - 5 la puterea a 20 -5 la puterea a 18)

Answer 1

[tex]A=11\cdot(5^{21}-5^{20}-5^{18})\\ A=11\cdot5^{18}(5^3-5^2-1)\\ A=11\cdot5^{18}(125-25-1)\\ A=11\cdot 5^{18}\cdot 99\\ A=11^2\cdot5^{18}\cdot 9\\ A=11^2\cdot(5^9)^2\cdot3^2\\ A=(11\cdot3\cdot5^9)^2[/tex]