Question

Rezolvați mi si mie astaaaaa

Answer 1

$x \circ \: y = xy + 2x + 2y + 2 \: ,x,y\:\in\:\mathbb{R}$

$a)x \circ y = (x + 2)(y + 2) - 2$

Metoda I (desfacem parantezele) :

$= x \times y + x \times 2 + 2 \times y + 2 \times 2 - 2$

$= xy + 2x + 2y + 4 - 2$

$= xy + 2x + 2y + 2$

Metoda II :

$x \circ y = xy + 2x + 2y + 2$

$= x(y + 2) + 2(y + 2) - 2$

$= (x + 2)(y + 2) - 2$

$b)x \circ ( - 2) = - 2$

$x \times ( - 2) + 2 \times x + 2 \times ( - 2) + 2 = - 2$

$- 2x + 2x - 4 + 2 = - 2$

$- 4 + 2 = - 2$

$- 2 = - 2 \: \: (A)$

$( - 2) \circ y = - 2$

$- 2 \times y + 2 \times ( - 2) + 2 \times y + 2 = - 2$

$- 2y - 4 + 2y + 2 = - 2$

$- 4 + 2 = - 2$

$- 2 = - 2 \: \: (A)$