razlika kvadratak - MIM-Sraga

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M-1-Razlika kvadrata Rješenja i kompletni postupak ( )( ) 7. Koristimo formulu za razliku kvadrata: A− B A+ B = A −B 2 2 1) ( )( ) x− y x+ y = x − y 2 2 ( )( ) 2 2 2 2) 1 1 1 1 x− x+ = x − = x − ( )( ) 2 2 2 3) 2 2 2 4 x− x+ = x − = x − ( )( ) 2 2 2 4) 3 3 3 9 x+ x− = x − = x − ( )( ) ( ) 2 2 5) 3a+ b 3a− b = 3a − b = 2 2 2 = ⋅ − = 2 2 ( a b)( a b) ( a) ( b) 3 = 9a −b 2 2 6) 2 − 3 2 + 3 = 2 − 3 = a 2 a 3 2 2 2 2 = ⋅ − ⋅ = 4a b 2 = − 9b 2 b ( xy z)( xy z) ( xy) ( z) 2 2 7) 2 − 5 2 + 5 = 2 − 5 = 2 x y 5 z 2 2 2 2 2 = ⋅ ⋅ − ⋅ = = 4xy −25z 2 2 2 ( x yz)( x yz) ( x) ( yz) 2 2 8) 4 + 3 4 − 3 = 4 − 3 = 4 x 3 y z 2 2 2 2 2 = ⋅ − ⋅ ⋅ = = 16x −9y z 2 2 2 ( ba c)( ba c) ( ba) ( c) 2 2 9) 3 − 7 3 + 7 = 3 − 7 = 3 b a 7 c 2 2 2 2 2 = ⋅ ⋅ − = = 9ba − 49 c = ili = 9ab −49c 2 2 2 2 2 2 M I M <strong>Sraga</strong> 2005 2
M-1-Razlika kvadrata Rješenja i kompletni postupak ( )( ) 7. Koristimo formulu za razliku kvadrata: A− B A+ B = A −B 2 2 10) 2 2 + − = − = ⎛1 ⎞⎛1 ⎞ ⎛1 ⎞ ⎜ x y⎟⎜ x y⎟ ⎜ x⎟ y ⎝2 ⎠⎝2 ⎠ ⎝2 ⎠ 1 2 1 = x − y 4 2 2 2 = ⋅x − y = 2 2 2 11) 2 2 − + = − = ⎛2 ⎞⎛2 ⎞ ⎛2⎞ ⎜ x⎟⎜ x⎟ ⎜ ⎟ x ⎝3 ⎠⎝3 ⎠ ⎝3⎠ 2 3 4 = −x 9 2 2 = − x = 2 2 3 3 2 3 ⎛ ⎞⎛ ⎞ ⎛ ⎞ 12) ⎜5a− b⎟⎜5a+ b⎟ = ( 5a) −⎜ b⎟ = ⎝ 4 ⎠⎝ 4 ⎠ ⎝4 ⎠ ( )( ) 2 2 13) 200 2 200 2 200 2 40000 4 39996 ( )( ) 2 2 14) 300 7 300 7 300 7 90000 49 89951 ( )( ) 2 2 15) 100 9 100 9 100 9 10000 81 9919 ( ) ( ) 2 2 16) 48 52 50 2 50 2 50 2 2500 4 2496 ( ) ( ) 17) 97⋅ 103 = 100−3 ⋅ 100+ 3 2 2 2 3 2 = 5 ⋅a − ⋅ b = 2 4 2 9 2 = 25a − b 16 − + = − = − = − + = − = − = − + = − = − = ⋅ = − ⋅ + = − = − = ( ) ( ) 2 = − = − = 2 2 100 3 10000 9 9991 ⋅ = − ⋅ + = − = − = 2 2 18) 195 205 200 5 200 5 200 5 40000 25 39975 M I M <strong>Sraga</strong> 2005 3
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