Question

Se considera expresia E(x,y)=x²+y²-6xy+2(2xy-17)- 5x+5y+40 unde x si y sunt numere naturale. a) Descompuneti expresia in produs de factori ireductibili b) Calculati valuarea expresiei stiind ca x-y=8 ​

Answer 1

Răspuns:

E(x,y)=x²+y²-6xy+2(2xy-17)- 5x+5y+40=

${x}^{2} + {y}^{2} - 6xy + 4xy - 34 - 5x + 5y + 40 \\ {x}^{2} + {y}^{2} - 2xy + 6 -5 (x - y) = \\ (x - y)^{2} - 5(x - y) + 6 =$

${(x - y)}^{2} - 2(x - y) + 1 - 5(x - y) + 5 = \\ ({x - y - 1})^{2} - 5(x - y - 1) = \\ (x - y - 1)(x - y - 1 + 5) = \\ (x - y - 1)(x - y + 4)$

E=(8-1)(8+4)=7×12=84