razlika kvadratak - MIM-Sraga

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