Vjezbe 1
Ponavljanje gradiva srednje skole
Potencije
Pravila za racunanje s potencijama
an am = an+m
(an)m = anm
an = 1an
an : am = an
am= an am = anm
a0 = 1 a 6= 0 (a b)n = an bn
man = a nm
a)
(2 a35 b4
)3(1
10a2 b4
)2
b)
(27 x7 y816 z14
)4:
(y7
18 x2 z3)5
c)
((2 a2 b1)2(2 a2 b1)1
)3:
((2 a2 b1)2(2 a2 b1)1
)1d) 4a7 (a+ b)5
e)
(4
x2
y
)2: 8
x5
y6
f)1
bc
a2 b c+ 1
ac
a b2 c+ 1
ab
a b c2
g)1
a+ bc+
1
a bc
Algebarski izrazi i razlomci
a) x2 + 10x+ 21
b) x3 + y3 + x2y + xy2
c)2a4 8a3b+ 8a2b2
a4 2a3b1
d)x3 + y3 + (x+ y)3
x2 y2
e)4
y + 2 3y 2 +
12
y2 4
f)x y
x2 + 4xy + 4y2+
3x
x2 4y2
g)5
4a 4 9a+ 41
20a2 20 4
5a+ 5
h)
(a3 + 1
3a2 3a +a+ 1
a 1)(
1
a+ 1 1 aa2 1
)
Linearne i kvadratne jednadzbe
a) 3(2x+ 1) = 7(x 1)b) x 18 = 5x+ 2(3 x)c) (x 2) 3 + (3x 1) 4 = (6x 8) 5
d)2x
3 x
2+ 2 =
x
3 x
e)x+ 3
4+3
2=
5x+ 27
9 7x 9
4+ 10
f)x+ 1
x 1 x 1x+ 1
=16
x2 1
g)
1
x 1 +2
x+ 34
x 1 2
x+ 3
= 1
h) (x+ 1)2 x 1 = 0i) 4x2 8x+ 5 = 0
j)x+ 1
2x2 3x 4x+ 1
4x2 + 6x=
10
4x2 9
k)
{x+ y = 8x y = 15
l)
{x y = 1
x3 y3 = 7m)
4x+ 13 +
x+ 1 =
3x+ 12
n)x 1 +2x+ 5 = 8
2
Linearne i kvadratne nejednadzbe
a)1
2x+ 3 > 5 +
1
3x
b)2x 5
2
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