ALGEBARSKI IZRAZI

M-1-Kvadrat binoma
Rješenja i kompletni postupak
34.
m n m m n n
( ) ( ) ( )
( ) ( )
2 2 2
+ = + ⋅ ⋅ + =
m⋅2 1 m n n⋅2
= 2 + 2 ⋅2 ⋅ 3 + 3 =
m
2 m+
1 n 2
( 2 ) 2 3 ( 3 )
2 2 2 2 2 2
Kvadriramo po pravilu: A+ B = A + 2⋅A⋅ B+ B i A− B = A −2⋅A⋅ B+
B
81) 2 3 2 2 2 3 3
2⋅ m 1+ m n 2⋅n
= 2 + 2 ⋅ 3 + 3 = =
= + ⋅ + =
= + ⋅ +
n m+
1 n n
4 2 3 9
m n m m n n
( ) ( ) ( )
83) 2 2 2 2 2 2 2
2 2 2
+ = + ⋅ ⋅ + =
2 2 2 2 2
m⋅2 1 m n n⋅2
= + ⋅ ⋅ + =
m
2 m+ n+
1 2
( 2 ) 2 ( 2 )
n
m m m m m m
( ) ( ) ( )
82) 3 5 3 2 3 5 5
2 2 2
− = − ⋅ ⋅ + =
( )
m⋅2 m m⋅2
= 3 −2⋅ 3⋅ 5 + 5 =
m
2 m 2
( 3 ) 2 15 ( 5 )
m m− m m m− m−
( ) ( ) ( )
1 2 2 1 1 2
+ = + ⋅ ⋅ + =
m⋅2 1 m m−1
2 2 2 2 2
2⋅ m 1+ m+ n 2⋅n 2⋅m
1+ m+ m−1
2 2 2 2 2
m m+ n+
1 n
4 2 4
n
2⋅m m 2⋅m
3 −2⋅ 15 + 5 =
= − ⋅ + =
= 9 −2⋅ 15 + 25
m m m
84) 2 2 2 2 2 2 2
= + + = = +
= + + =
= + +
m n m m n n
( ) ( ) ( )
85) 3 3 3 2 3 3 3
2 2 2
− = − ⋅ ⋅ + =
m⋅ 2 m+ n n⋅2
= 3 −2⋅ 3 + 3 =
2⋅ m m+ n 2⋅n
= 3 −2⋅ 3 + 3 =
m
2 m+
n 2
( 3 ) 2 3 ( 3 )
= − ⋅ + =
+
= 9 −2⋅ 3 + 9
m m n n
m+ m− m+ m+ m− m−
( ) ( ) ( )
1 1 2 1 2 1 1 1 2
86) 2 + 2 = 2 + 2⋅2 ⋅ 2 + 2 =
= 2
( m 1)
+ ⋅2 1 m+ 1 m−1
m−1 ⋅2
n
( )
⋅ ( m+ ) 1+ m+ 1+ m−1
⋅( m−
)
2 1 2 1
m
2 2m+
1 2
( 2 ) 2 ( 2 )
+ 1 m−1
m+ 1 2m+ 1 m−1
n −n n n −n −n
( ) ( ) ( )
1 2 2 1 1 2
+ = − ⋅ ⋅ + =
n
2 2 2
( 2 ) 2 ( 2 )
+ 2 ⋅2 ⋅ 2 + 2 =
= 2 + 2 + 2 =
= + + =
= 4 + 2 + 4
87) 2 2 2 2 2 2 2
( −n)
n⋅2 1 n 1−n
1 ⋅2
= 2 −2 ⋅2 ⋅ 2 + 2 =
⋅( −n)
2⋅
n 1+ n+ 1−n
2 1
2 2 2
= − + =
n
= 4 − 4+
4
1−n
1−n
= − + =
m
( m−
)
1 ⋅2
= + ⋅ ⋅ + =
m
2 2m
2
( 2 ) 2 ( 2 )
m
m 2 m−1
4 ( 2 ) 4
m m m−1
= 4 + 4 + 4 =
m
= 24 ⋅ + 4
m−1
⋅( m−
)
2 1
+ 2 =
m−1
= + + =
= + + =
M.I.M.-Sraga -2003./2013.
www.mim-sraga.com
17
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