ALGEBARSKI IZRAZI
kvadrat zbroja - MIM-Sraga
kvadrat zbroja - MIM-Sraga
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M-1-Kvadrat binoma<br />
Rješenja i kompletni postupak<br />
34.<br />
Kvadriramo po pravilu:<br />
To pravilo možemo pisati i ovako:<br />
( x y) ( x) x y ( y)<br />
( ) ( )<br />
2 2 2<br />
29) 3 − 4 = 3 −2⋅3 ⋅ 4 + 4 =<br />
2 2 2 2<br />
= x − xy+ y =<br />
2 2<br />
2 2 2 2 2 2<br />
A+ B = A + 2⋅A⋅ B+ B i A− B = A −2⋅A⋅ B+<br />
B<br />
3 24 4<br />
= 9x − 24xy+<br />
16y<br />
( ) i ( )<br />
2 2 2 2 2<br />
I + II = I + 2⋅I ⋅ II + II I − II = I −2⋅I ⋅ II + II<br />
2<br />
2<br />
( a+ b) = ( a)<br />
25a 7b ( 7b)<br />
30) 5 7 5<br />
2 2<br />
+ ⋅ ⋅ + =<br />
2 2 2 2<br />
= + + =<br />
5 a 70ab 7 b<br />
= 25a + 70ab+<br />
49b<br />
2 2<br />
( ) ( )<br />
2 2 2<br />
31) 3m+ n = 3m + 2⋅3m⋅ n+ n =<br />
2 2 2<br />
= + + =<br />
3 m 6mn n<br />
= 9m + 6mn+<br />
n<br />
2 2<br />
( m n) ( m) m n ( n)<br />
2 2 2<br />
32) 2 − 5 = 2 −2⋅2 ⋅ 5 + 5 =<br />
2 2 2 2<br />
= − + =<br />
2 m 20mn 5 n<br />
= 4m − 20mn+<br />
25n<br />
2 2<br />
( ) ( )<br />
2 2 2 2 2 2<br />
33) 0,2x+ 3 = 0,2x + 2⋅0,2⋅x⋅ 3+ 3 = 0,2 x + 1,2x+ 9 = 0,04x<br />
+ 1,2x<br />
+ 9<br />
Još jednom taj isti zadatak:<br />
( ) ( )<br />
2<br />
2 0,2 3 1,2 0,2 0,2 0,2 0,04<br />
2 2 2<br />
2 2 2<br />
0,2 1,2 9 0,2 0,2 0,2 0,04<br />
2<br />
0,04 1, 2 9<br />
Uputa:<br />
33) 0,2x+ 3 = 0,2x + 2⋅0,2⋅x⋅ 3+ 3 = → 2⋅0,2⋅ 3 = 1,2<br />
= x + x+ = → = ⋅ =<br />
= x + x+<br />
↓<br />
↓<br />
⋅ ⋅ = = ⋅ =<br />
( ) ( )<br />
2 2 2<br />
34) 1,2x+ 0,3 = 1,2x + 2⋅1,2x⋅ 0,3+ 0,3 = → 2⋅1,2⋅0,3 = 0,72<br />
= x + ⋅ ⋅ ⋅ x+ = → = ⋅<br />
2 2 2<br />
1, 2 2 1, 2 0, 3 0, 09 1, 2 1, 2 1, 2 1,<br />
= x + x+<br />
2<br />
1,44 0,72 0,09<br />
=<br />
44<br />
M.I.M.-Sraga -2003./2013.<br />
www.mim-sraga.com<br />
7<br />
© M.I.M-Sraga centar za poduku<br />
mim-sraga@zg.htnet.hr<br />
tel-01-4578-431
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