Question

STIIND CA 12X-5Y/3X =2/3 CALCULATI X/Y SI X PATRAT+XY / YPATRAT​

Answer 1

Explicație pas cu pas:

$\dfrac{12x - 5y}{3x} = \dfrac{2}{3}$

$3(12x - 5y) = 2 \cdot 3x$

$12x - 5y = 2x \\ 12x - 2x = 5y$

$10x = 5y \iff 2x = y \implies \dfrac{x}{y} = \dfrac{1}{2}$

$\dfrac{ {x}^{2} + xy}{ {y}^{2} } = \dfrac{ {x}^{2}}{ {y}^{2} } + \dfrac{xy}{ {y}^{2} } = {\bigg(\dfrac{x}{y} \bigg)}^{2} + \dfrac{x}{y} = \\ = {\bigg(\dfrac{1}{2} \bigg)}^{2} + \dfrac{1}{2} = \dfrac{1}{4} + \dfrac{1}{2} = \dfrac{1 + 2}{4} = \dfrac{3}{4}$