Question

solve : xy/(x+y)=14;xy/(x-y)=6​

Answer 1

Answer:

x = -21 and y = 42/5

Step-by-step explanation:

$=> \frac{xy}{x+y} =14 \\\\=> \frac{xy}{x-y} =6 \\\\\\ div ide \ above \ equations, \\\\ =>\frac{\frac{xy}{x+y}} {\frac{xy}{x-y}} =\frac{14}{6} \\\\=>\frac{x-y}{x+y} =\frac{7}{3} \\\\=> \frac{x+y}{x-y} =\frac{3}{7} \\\\=>\frac{x}{y} =\frac{3+7}{3-7} \\\\=>\frac{x}{y} =\frac{10}{-4} \\\\=>\frac{x}{y} =\frac{-5}{2} \\\\=>2x=-5y \\\\=>x=\frac{-5y}{2} \\\\ \\ \frac{xy}{x-y} =6 \\\\ \frac{(\frac{-5y}{2})(y) }{\frac{-5y}{2}-y} =6$

$\frac{-5y^{2}}{2} / \frac{-7y}{2} =6 \\\\ \frac{5y}{7}=6 \\\\ 5y=42 \\\\ y=\frac{42}{5} \\\\=>x=\frac{-5y}{2} \\\\ x=(\frac{-5}{2})(\frac{42}{5})\\\\x=-21$

∴ x = -21 and y = 42/5

HOPE IT HELPS..!

Answer 2

Answer:

y=42/5,x=-21

Step-by-step explanation:

xy/(x+y)=14...(1)

xy/(x-y)=6......(2)

Our goal is to simplify this equation..

Therefore,(1)/(2) is

(xy/(x+y))/xy/(x-y)=14/6

x-y/(x+y)=14/6

Using compenendo and dividendo,

2x/-2y=5/2

x=-5/2y...(3)

Substituting (3) in (2),

(-5y/2y)/(-5/2y-y)=6

(-5y^2/2)/-7y/2=6

5y=42

y=42/5...(4)

Substituting (4) in (3)..

x=-5/2(42/5)

x=-21

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