Question

Відомо, що
$\frac{x - y} {x + y} = \frac{12}{13}$
Знайдіть
$\frac{x {}^{2} }{y {}^{2} }$

Answer 1

$\frac{x - y}{x + y} = \frac{12}{13}$

$(x - y)*13 = (x + y)*12$

$13x - 13y = 12x + 12y$

$13x - 12x = 13y + 12y$

$x=25y$

$\frac{x}{y} =25$

$\frac{x {}^{2} }{y {}^{2} }= (\frac{x}{y} )^{2} = 25^{2}= 625$

Ответ: 625.

Answer 2

x+yx−y​=1312​

(x - y)*13 = (x + y)*12(x−y)∗13=(x+y)∗12

13x - 13y = 12x + 12y13x−13y=12x+12y

13x - 12x = 13y + 12y13x−12x=13y+12y

x=25yx=25y

\frac{x}{y} =25yx​=25

\frac{x {}^{2} }{y {}^{2} }= (\frac{x}{y} )^{2} = 25^{2}= 625y2x2​=(yx​)2=252=625

Ответ: 625