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1) 2) 3) 2 3 2+ 3 5 2 4 6 2+ 4+ 6 12 Kompletna rješenja s postupkom 2 5 2 5 22 ⋅ + 26 ⋅ + 53 ⋅ 31 + 2+ 3 2 2 3 2 3⋅2 6 4) x : x = x = x 4 2 4−2 2 5) x : x : x = x = x 7 2 3 7−2−3 2 6) x ⋅ x : x = x = x 7 8 9 7+ 8−9 6 8 x 7) = x : x = x = x 3 x 8) 9) 10) x ⋅ x = x = x x ⋅x ⋅ x = x = x x ⋅x ⋅ x = x = x = x 8 3 8−3 5 3 2 2⋅3 6 ( x ) = x = x 4 5 3 345 ⋅ ⋅ 60 (( x ) ) = x = x 6 2 5 2 2 2⋅6⋅ (( x ) ) ⋅ ( x ) = x 5 3 5 (( ) ) ( ) 3 3 ( ) ( ) 2 2⋅ 5 24 10 24+ 10 34 11) x : x = x : x = x : x = x = x 2 4 2⋅5⋅3 4⋅5 30 20 30−20 10 12) 2ab = 2 ⋅a ⋅ b = 8⋅a ⋅ b = 8a b 13) 15) 16) ⋅ x = x ⋅ x = x = x 2 3 3 2 3 2⋅3 3 6 4 4 4 4 2 3 2 3 8 12 4 ⎛2 ⎞ 2 16 ⎜ xy⎟ = ⋅ ( x) ⋅ ( y) = xy ⎝3 ⎠ 3 81 ( ) 3 3 2 3 3 2 2 3⎞ 2 2 3 2 2 2 6 9 2 −1 8⋅a ⋅b 1 4⋅2⋅a ⋅a ⋅b ⋅b 1 2⋅a ⋅b = ⋅ = ⋅ = ⋅a ⋅b ⋅a ⋅b 6 9 2 4 4 5 4 5 2 4 2 4 27 4 27 4 27 −2 3 2 3 2 3 2+ 3 5 3 2 3 2+ 3 5 ( a ) ( ) ( ) ( y ) ( ) 3 2 3 2 2 2 2 2 2 2 6 ⎛a ⎞ ⎛ y ⎞ ⎛ y ⎞ y a 17) ⎜ ⎟ ⋅ ⎜ ⎟ : ⎜ ⎟ = ⋅ : = ⎝ y ⎠ ⎝a ⎠ ⎝a ⎠ y a a y 3 3 4 3 2 2 3 3 4 9 100 Elementarnih zadataka ⎛2 2 8 4 14) ⎜ a b ⎟ :( 2 ab ) = ⋅ 3 ( a ) ⋅( b ) : 2 ⋅a ⋅ ( b ) = ⋅a ⋅b :( 4⋅a ⋅ b ) = ⎝3 ⎠ 3 27 ⎛ x⎞ ⎜ ⎟ ⎝ y⎠ = y x ⎛ x⎞ ⎛ y⎞ ⎛ y⎞ y y y y y ⎜ ⎟ ⋅ ⎜ ⎟ = ⎜ ⎟ ⋅ = ⋅ = = ⎝ y⎠ ⎝ x⎠ ⎝ x⎠ x x x x x y ⋅a a a = = = y ⋅y ⋅y y y 2 8 8 8 9 2 2 9+ 2 11 −1 −2 −3 2 3 2 4 6 2 8 y y a y a ⋅ : = ⋅ ⋅ = 6 8 9 6 4 a a y a y ⎛2⎞ ⎛1⎞ ⎛1⎞ 3 ⎛3⎞ ⎛2⎞ 3 3 3+ 2 5 18) ⎜ ⎟ + ⎜ ⎟ − ⎜ ⎟ = + ⎜ ⎟ − ⎜ ⎟ = + 9 − 8 = + 1 = = ⎝3⎠ ⎝3⎠ ⎝2⎠ 2 ⎝1⎠ ⎝1⎠ 2 2 2 2 © −1 0 0 0 1 ⎛1⎞ 3 19) 27 x y 2 1112 2 3 6 ⋅ ⋅ ⋅ ⋅ ⎜ ⎟ = ⋅ ⋅ ⋅ ⋅ = ⋅ = ⎝3⎠ 1 0 −1 ⎛1⎞ ⎛1⎞ 20) y ⋅2 ⋅⎜ ⎟ ⋅⎜ ⎟ ⎝2⎠ ⎝5⎠ 1 12 M I M SRAGA 1999 / 2004 −1 1 1 5 1 1⋅5⋅1 5 ⋅ = ⋅ ⋅ ⋅ ⋅ = = −3 2 1 2 2 1 2 3 2 ⋅ 2 ⋅ 8 32
100 Elementarnih zadataka 21) x 1 2 = x 22) 23) x 1 − 2 1 1 = = 1 2 x x 2 1 1 2⋅ 3 3 2 3 3 2 ( ) x = x = x = x 24) x 3 − 4 1 1 1 = = = x 3 1 4 3 4 4 x 3 ( x ) 25 1 ) 2 36 = 36 = 2 6 = 6 26 1 ) 4 4 4 4 16 = 16 = 2 = 2 27 ) 1 2 ⎛25 ⎞ 25 25 5 ⎜ ⎟ = = = ⎝49 ⎠ 49 49 7 28) 1 4 4 16 4 16 2 2 2 = 4 = 4 = 4 = 4 ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎝81⎠ 81 3 ⎝3 ⎠ 3 29) 1 1 − 2 2 ⎛64 ⎞ ⎛49 ⎞ 49 49 7 ⎜ ⎟ = ⎜ ⎟ = = = ⎝49 ⎠ ⎝64 ⎠ 64 64 8 30) 3 3 3 3 3 − 2 2 2 2 2 2⋅ 3 2 2 3 ⎛ 9 ⎞ ⎛16⎞ ⎛4 ⎞ ⎛⎛4⎞ ⎞ ⎛4⎞ ⎛4⎞ 4 64 ⎜ ⎟ = ⎜ ⎟ = ⎜ ⎟ = ⎜ ⎟ = ⎜ ⎟ = ⎜ ⎟ = = ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎜⎝ ⎠ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 3 16 9 3 3 3 3 3 27 31 2 ) 10 ⋅ 10 = 10⋅ 10 = 10 = 10 32 3 3 3 3 3 3 ) 3 ⋅ 9 = 3⋅ 9 = 27 = 3 = 3 33 4 4 4 4 4 4 ) 2 8 2 8 16 2 2 ⋅ = ⋅ = = = 34) x ⋅ x = x ⋅ x = x = x 5 2 5 3 5 2 3 5 5 35 6 5 6 6 5 2 6 5−2 6 3 23 ⋅ 3 2 ) x : : x = x x = x = x = x = x = x © M I M SRAGA 1999 / 2004 13
Page 1 and 2: 100 Elementarnih zadataka **** MLAD
Page 3 and 4: STO ELEMENTARNIH ZADATAKA KOJE BI S
Page 5 and 6: Koristeći formule koje smo upravo
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Page 11: 100 Elementarnih zadataka 2 2 3x y+
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