Răspuns:
Explicație pas cu pas:
a)
(1/2 + 1/6)^2 + (1/12)^2
= (3/6 + 1/6)^2 + (1/12)^2
= (4/6)^2 + (1/12)^2
= (2/3)^2 + (1/12)^2
= (8/12)^2 + (1/12)^2
= 64/144 + 1/144 = 65/144
b)
(1/2 + 1/6 + 1/12)^2 = (6/12 + 2/12 + 1/12)^2 = (9/12)^2 = (3/4)^2 = 9/16
c)
(1/2 + 1/6)^2 - (1/12)^2
= (3/6 + 1/6)^2 - (1/12)^2
= (4/6)^2 - (1/12)^2
= (2/3)^2 - (1/12)^2
= (8/12)^2 - (1/12)^2
= 64/144 - 1/144 = 63/144
d)
(1/2 + 1/6 + 1/12)*(1/2 + 1/6 - 1/12)
= (6/12 + 2/12 + 1/12)*(6/12 + 2/12 - 1/12)
= 9/12 * 7/12
= 3/4 * 7/12 = 21/48 = 7/16
e)
1/4 + 1/36 - 1/144 = 36/144 + 4/144 - 1/144 = 39/144 = 13/48
f)
1/2 - (1/6 - 1/12)^2 = 1/2 - (2/12 - 1/12)^2 = 1/2 - 1/144 = 72/144 - 1/144 = 71/144
