2 i 3 ISPIT ZNANJA

ALGEBARSKI IZRAZI – test br.2. i 3.
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6.
( x ) 2 x y ( y )
( x y )
( ) ( ) ( )
( ) ( )
a) x − 2x y + y = x −2 ⋅x ⋅ y + y = → x = x = x , y = y = y
6 3 2 4 32 ⋅ 3 2 22 ⋅ 6 32 ⋅ 3 2 4 22 ⋅ 2 2
= −
= −
3 2 3 2 2 2
3 2 2
Još jednom isti zadatak :
⋅ ⋅ + =
x − 2x y + y = x −2⋅x ⋅ y + y = x −2⋅x ⋅ y + y = x − y
6 3 2 4 3⋅2 3 2 2⋅2 3 2 3 2 2 2 3 2 2
↓ ↓ ↓ ↑ ↑
( )
− 2⋅ ⋅ + = −
2 2
A A B B A B
2
2 2
b) 20xy−4x − 25y = −4x
+ 20xy
− 25y
=
2 2
2 2
( x xy y )
2 2 2 2
( x x y y )
=−1⋅ 4 − 20 + 25 =
=−1⋅ 2 ⋅ −2⋅2⋅5⋅ ⋅ + 5 ⋅ =
2 2
(( x) x y ( y)
)
=−1⋅ 2 −2⋅2 ⋅ 5 + 5 =
( x y)
=−1⋅ 2 −5
2
7.
7 4 5 3 4 2 4 3 2 2 4 1 2 1 4 2
a) a b + a b − a b = a ⋅a ⋅b ⋅ b + a ⋅a ⋅b ⋅b −a ⋅b
⋅ 1=
a a b b a a b b a b
4 3 2 2 4 1 2 1 4 2
= ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ − ⋅ ⋅ =
( 1)
( 1)
a b a b a b
4 2 3 2 1 1
= ⋅ ⋅ ⋅ + ⋅ − =
4 2 3 2
ab ab ab
= + −
1
3 2 2 3 2 2
b) x y− 6x y + 9xy = x⋅x ⋅y−6⋅x⋅x⋅y⋅ y+ 9⋅x⋅y⋅ y =
(
2
6 9
2)
(
2
6 9
2)
2
( x 2 x 3y 3y
2
)
= x⋅y⋅ x − xy+ y =
= x⋅y⋅ x − xy+ y =
= xy⋅ − ⋅ ⋅ + ( ) =
( 3 )
= xy⋅ x − y
2
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