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M-1-Razlika kvadrata<br />
Rješenja i kompletni postupak<br />
( )( )<br />
7. Koristimo formulu za razliku kvadrata: A− B A+ B = A −B<br />
2 2<br />
( )( ) ⎡( ) ⎤ ⎡<br />
⎣<br />
⎦ ⎣( )<br />
2 3 2 6 2<br />
= ( 2x + 3y ) − ( 5z<br />
) =<br />
( 2x ) 2 2x 3y ( 3y ) 5 ( z )<br />
2 2 2 2 3 2 3 2 6⋅2<br />
2 ( x ) 12x y 3 ( y ) 25 z<br />
2 3 6 2 3 6 2 3 6 2 3 6<br />
59) 2x + 3y + 5z 2x + 3y − 5z = 2x + 3y + 5z ⋅ 2x + 3y − 5z<br />
⎤<br />
⎦<br />
=<br />
Još malo upute:<br />
2 2 2 3 3 2 2 6 2<br />
= + ⋅ ⋅ + − ⋅ =<br />
= ⋅ + + ⋅ − ⋅ =<br />
4 2 3<br />
4 12 9<br />
= x + x y + y<br />
2 3 6 2 3 6<br />
( 2x + 3y + 5z )( 2x + 3y − 5z<br />
) =<br />
[ ( 2x 3y ) 5 z ][ ( 2x 3y ) 5 z ] ( 2x 3y ) ( 5z<br />
)<br />
( ) ( )<br />
− 25z<br />
6 12<br />
2 3 6 2 3 6 2 3 2 6 2<br />
= + + ⋅ + − = + − =<br />
<br />
↓<br />
↓<br />
↓ ↓ ↑ ↑<br />
A + B ⋅ A − B = A − B<br />
2 2<br />
I dalje kvadriramo:<br />
( 2x ) 2 2x 3y ( 3y ) 5 ( z )<br />
2 2 2 2 3 2 3 2 6⋅2<br />
2 ( x ) 12x y 3 ( y ) 25 z<br />
2 2 2 3 3 2 2 6 2<br />
= + ⋅ ⋅ + − ⋅ =<br />
= ⋅ + + ⋅ − ⋅<br />
4x 12x y 9y 25z<br />
4 2 3 6 12<br />
= + + − =<br />
=<br />
2 3 2 3 2 3 2 3<br />
( x y z )( x y z ) x ( y z ) x ( y z )<br />
2 2 3 2<br />
= ( 5x) −( 4y − z ) =<br />
2 2 2 2 2 3 3 2<br />
5 x ⎡( 4y ) 2 4y z ( z ) ⎤<br />
⎣<br />
⎦<br />
2 2 2 2 2 3 3⋅2<br />
= 25x −⎡4 ( y ) 8y z z ⎤<br />
⎣<br />
⋅ − +<br />
⎦<br />
=<br />
2 4 2 3 6<br />
= 25x −( 16y − 8y z + z ) =<br />
60) 5 − 4 + 5 + 4 − = ⎡5 − 4 − ⎤⋅ ⎡5 + 4 − ⎤<br />
⎣ ⎦ ⎣ ⎦<br />
=<br />
= ⋅ − − ⋅ ⋅ + =<br />
= 25x −16y −8y z −z<br />
2 4 2 3 6<br />
M I M <strong>Sraga</strong> 2005<br />
12