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