Odpowiedź:
zad 6
a)
o - obwód = 2(∛16 + ∛4) = 2∛4(∛4 + 1)
P - pole = ∛16 * ∛4 = ∛(16 * 4) = ∛64 = 4
b)
o = 5 + √5 + √20 = 5 +√5 +√(4 * 5) = 5 + √5 + 2√5 = 5 + 3√5
P = √5 * √20 = √(5 * 20) = √100 = 10
c)
o = √32 + 4√2 + √2 + 5√2 = √(16 *2) + 10√2 = 4√2 + 10√2 = 14√2
P = 1/2 * (√32 + √2) * 4√2 = 1/2 * (4√2 + √2) * 4√2 = 5√2 * 2√2 = 5 * 2 * 2 = 20
d)
o = 4 * √75 = 4√75 = 4√(25 * 3) = 4 * 5√3 = 20√3
P = 1/2 * 2(8√3 + 6√3) = 8√3 + 6√3 = 14√3
e)
o = 6√5 + 2√10 + 3√5 + 5 = 9√5 + 2√10 + 5
P = 1/2 * (6√5 + 3√5) * 2√5 = 1/2 * 9√5 * 2√5 = 9√5 * √5 = 9 * 5 = 45
f)
o =2√2 + 2 + √32 + 2√3 = 2√2 + 2 + √(16 * 2) + 2√3 = 2√2 +2 + 4√2 + 2√3 =
= 2√3 + 6√2 + 2 = 2(√3 + √2 + 1)
P = 1/2 * (2√2 + √32) * 2 = 2√2 + 4√2 = 6√2
