ALGEBARSKI IZRAZI

M-1-Kvadrat binoma
Rješenja i kompletni postupak
34. Kvadriramo po pravilu: A+ B = A + 2⋅A⋅ B+ B i A− B = A −2⋅A⋅ B+
B
( ) ( )
2 2 2 2 2 2
2 2 2
⎛ 2 ⎞ ⎛3⋅ 3+
2 5 ⎞ ⎛11 1 ⎞
47) ⎜3 x− 0,5y⎟ = ⎜ x− y⎟ = ⎜ x− y⎟
=
⎝ 3 ⎠ ⎝ 3 10 ⎠ ⎝ 3 2 ⎠
2 2
⎛11 ⎞ 11 1 ⎛1
⎞
= ⎜ x⎟ −2⋅ ⋅x⋅ ⋅ y+ ⎜ y⎟
=
⎝ 3 ⎠ 3 2 ⎝2
⎠
2 2
11 2 11 1 2
= x − xy+ y =
2 2
3 3 2
121 2 11 1 2
= x − xy+
y
9 3 4
48)
2 2 2
⎛1
3 ⎞ ⎛1 ⎞ 1 3 ⎛3
⎞
⎜ xz − y⎟ = ⎜ xz⎟ −2⋅ ⋅x⋅z⋅ ⋅ y+ ⎜ y⎟
=
⎝4
2 ⎠ ⎝4 ⎠ 4 2 ⎝2
⎠
2 2
1 2 2 1 3 3 2
= xy −2⋅ ⋅ ⋅xzy ⋅ ⋅ + y =
2 2
4 4 2 2
1 2 2 3 9 2
= xy − xzy+
y
16 4 4
( ) ( ) ( )
x + = x + ⋅x ⋅ + = → x = x = x
2 2 2 2 2 2 2 2 2⋅2 4
49) 1 2 1 1 po pravilu:
22 ⋅ 2
= + + =
x
2x
1
4 2
= + +
x
2x
1
( a )
= a
n m n⋅m
2
( ) ( )
2 2 2 2 2
50) x − 2 = x −2⋅x
⋅ 2+ 2 =
= x
x
− 4x
+ 4 =
22 ⋅ 2
4x
4
4 2
= − +
2
( x ) x ( x )
51) 3 3 2 3
4 2 4 4 2
− = − ⋅ ⋅ + =
x
x
4 4⋅2
= 9− 6 + =
= 9− 6x
+ x
4 8
M.I.M.-Sraga -2003./2013.
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