Question

ex 11 cu tot cu rezolvare vă rog ​

Answer 1

Răspuns:

a) x = 6 + 12 + 18 +...+ 288

x = 6(1 + 2 + 3 +... +48)

x = 6×(48×49)/2

x = 7056 = 84^2 pătrat perfect =>rad7056 = 84

b) x = 4 + 8 + 12 +... +196

x = 4(1+2+3+...+49)

x = 4×(49×50)/2

x = 4900 = 70^2 pătrat perfect =>rad4900 = 70

c) x = 1 + 3 + 5 +... +1001

1001 = 2n-1

2n = 1002

n = 501

x = n^2 = 501^2 pătrat perfect =>rad251001 = 501

d) x = 1 + 3 + 5 + 2021

2021 = 2n-1

2n = 2022

n = 1011

x = n^2 = 1011^2 pătrat perfect =>rad1022121 = 1011

e) x = 1203 + 2 + 4 + 6 +... +2404

x = 2(1+2+3+...+1202) + 1203

x = 2×(1202×1203)/2 + 1203

x = 1446006 + 1203

x = 1447209 = 1203^2 pătrat perfect =>rad1447209 = 1203