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20 Fie A= (0,5x²+3,5xy+3)-(2,7x²+1,75+1,3xy)-(1,25+2,2xy-3,2x²)
Aratati ca A este patrat perfect pentru orice valori ale numerelor naturale x si y.
24 Scrie numarul A=(4x²-9+3y²)-(3x²+2y²)+(14-y²) ca suma de doua patrate


Răspuns :

 A= (0,5x²+3,5xy+3)-(2,7x²+1,75+1,3xy)-(1,25+2,2xy-3,2x²) =
=
0,5x²+3,5xy+3-2,7x²-1,75-1,3xy-1,25-2,2xy+3,2x² =
=
0,5x²-2,7x²+3,2x²+3,5xy-1,3xy-2,2xy+3-1,75-1,25 =
=3,7x²-2,7x²+3,5xy-3,5xy+3-3 =
=x²

A=(4x²-9+3y²)-(3x²+2y²)+(14-y²) =
=4x²-9+3y²-3x²-2y²+14-y² =
=x²-9+14 =
=x²+5=
=x²+(√5)²