soluÅ£ii Åi barem
soluÅ£ii Åi barem
soluÅ£ii Åi barem
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Concursul interjudetean de matematica al Revistei SINUSEditia a II-a, Suceava, 18 noiembrie 2006Etapa finalaClasa a VII-a⎧1. a) Determinati elementele multimii: { } 2 x + 5⎫M = ⎨x∈ \ 2 | ∈ ⎬.⎩¢ x − 2¢⎭b) Stiind ca numerele întregi x, y, z verifica relatia xy= z 2+ z( x− y)− 5, aflati x+y .SINUS 2(5)/2006Solutie:x− 2/2x+ 5⇒x−2/2 x− 2 + 9⇒ x−2/9⇒x−2∈ ± 1, ± 3, ± 9 ………………….1pa) ( ) { }x∈{ −7, − 1,1,3,5,11}………………………………………………………………………1pb) xy= z 2+ z( x− y) −5⇔ ( x+ z)( y− z)= 5………………………………………....…2p( x z)( y z) ( 5)( 1) ( 1)( 5) ( 1)( 5) ( 5)( 1)+ − = − − = + + = − − = + + ……………………………2pFinalizare x+ y = 6……………………………………………………………………….1p