Question

poate cineva sa ma ajute la una dintre astea? doar una, nu am preferință (coroana+30p)​

Answer 1

9.

$\frac{x}{3} = \frac{y}{7} \: \: inseamna \: ca \: 7x = 3y \: deci \: x = \frac{3}{7} y$

$a) \: \frac{x}{2y} = \frac{ \frac{3}{7}y }{2y} = \frac{7y}{6y} = \frac{7}{6}$

$b) \: \frac{3x}{y} = \frac{3 \times \frac{3}{7} y}{y} = 3 \times \frac{3}{7} = \frac{9}{7}$

$c) \: \frac{x + y}{y - x} = \frac{ \frac{3}{7} y + y}{y - \frac{3}{7} y} = \frac{ \frac{3}{7}y + \frac{7}{7} y}{ \frac{7}{7}y - \frac{3}{7}y } = \frac{ \frac{10}{7}y }{ \frac{4}{7}y } = \frac{10}{7} \times \frac{7}{4} = \frac{10}{4}$

$d) \: \frac{2x + y}{x + 2y} = \frac{2 \times \frac{3}{7} y + \frac{7}{7} y}{ \frac{3}{7}y + \frac{14}{7} y} = \frac{ \frac{13}{7} y}{ \frac{17}{7}y } = \frac{13}{7} \times \frac{7}{17} = \frac{13}{17}$

$e) \: \frac{x^{2} + {y}^{2} }{xy} = \frac{ (\frac{3}{7})^{2} {y}^{2} + {y}^{2} }{ \frac{3}{7} {y}^{2} } = \frac{ \frac{9}{49} {y}^{2} + \frac{49}{49} {y}^{2} }{ \frac{3}{7} {y}^{2} } = \frac{ \frac{58}{49} {y}^{2} }{ \frac{3}{7} {y}^{2} } = \frac{58}{49} \times \frac{7}{3} = \frac{29}{3}$

$f) \: \frac{(x + y)^{2} }{4xy} = \frac{( \frac{3}{7} + y)^{2} }{4 \times \frac{3}{7} {y}^{2} } = \frac{ \frac{9}{49} + \frac{6}{7} y + {y}^{2} }{ \frac{12}{7} {y}^{2} } = \frac{9 + 42y + 49 {y}^{2} }{49} \times \frac{7}{12 {y}^{2} } = \frac{9 + 42y + 49 {y}^{2} }{24 {y}^{2} }$