Question

daca x, y apartin R* si 2x = 3y, calculati: 6x - 9y - 2, 3x/y - 5 si x^2 - y^2 / xy. dau coroana

Answer 1

2x=3y => x=3y/2.

6×3y/2 -9y -2=18y/2 -9y-2=9y-9y-2=-2.

(3×3y/2)/y -5=9y/2 × 1/y -5=9/2 -5=4,5-5=-0,5.

(3y/2)²-y²/(3y/2)×y=(9y²/4) -y²/(3y²/2)=(9y²-4y²/4) × 2/3y²=

=5y²/4 × 2/3y²=5/2 x 1/3=5/6.

Answer 2

$\it 2x=3y\ \ \ \ \ \ (*)\\ \\ \\ a)\ \ 6x-9y-2=3(2x-3y)-2\ \stackrel{(*)}{=}\ 3(2x-2x)-2=3\cdot0-2=-2\\ \\ \\ b) \ \ \dfrac{^{3)}3x}{\ \ y}-5=\dfrac{9x}{3y}-5\ \stackrel{(*)}{=}\ \dfrac{9x}{2x}-5=\dfrac{9}{2}-5=4,5-5=-0,5\\ \\ \\ c)\ \ \dfrac{x^2-y^2}{xy}=\dfrac{x^2}{xy}-\dfrac{y^2}{xy}=\dfrac{^{3)}x}{\ y}-\dfrac{^{3)}y}{\ x}=\dfrac{3x}{3y}-\dfrac{3y}{3x}\ \stackrel{(*)}{=}\ \dfrac{3x}{2x}-\dfrac{2x}{3x}=\dfrac{^{3)}3}{2}-\dfrac{^{2)}2}{3}=\\ \\ \\=\dfrac{9-4}{6}=\dfrac{5}{6}$