What is x/y-y/x = 5/6 ,x^2-y^2=5 ?

The solution to x/y-y/x = 5/6 ,x^2-y^2=5 is

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x/y-y/x = 5/6 ,x^2-y^2=5

Solution

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}, x^{2} - y^{2} = 5

Solution

x = 3, x = - 3, x = 2 i, x = - 2 i, y = 2 y = - 2 y = - 3 i y = 3 i

Solution steps

[\frac{x}{y} - \frac{y}{x} = \frac{5}{6} x^{2} - y^{2} = 5]

Isolate

x

for

\frac{x}{y} - \frac{y}{x} = \frac{5}{6} : x = \frac{3 y}{2}, x = - \frac{2 y}{3}

Plug the solutions

x = \frac{3 y}{2}, x = - \frac{2 y}{3}

into

x^{2} - y^{2} = 5

For

x^{2} - y^{2} = 5

, subsitute

x

with

\frac{3 y}{2} : y = 2, y = - 2

For

x^{2} - y^{2} = 5

, subsitute

x

with

- \frac{2 y}{3} : y = - 3 i, y = 3 i

Plug the solutions

y = 2, y = - 2, y = - 3 i, y = 3 i

into

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

For

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

, subsitute

y

with

2 : x = 3, x = - \frac{4}{3}

For

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

, subsitute

y

with

- 2 : x = - 3, x = \frac{4}{3}

For

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

, subsitute

y

with

- 3 i : x = - \frac{9}{2} i, x = 2 i

For

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}

, subsitute

y

with

3 i : x = - 2 i, x = \frac{9}{2} i

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

\frac{x}{y} - \frac{y}{x} = \frac{5}{6}, x^{2} - y^{2} = 5

are

x = 3, x = - 3, x = 2 i, x = - 2 i, y = 2 y = - 2 y = - 3 i y = 3 i

Popular Examples

f(x)=x^2-2x+3,f(x)=-2x+19

f (x) = x^{2} - 2 x + 3, f (x) = - 2 x + 19

((x+y))/((x-y))+((x-y))/((x+y))= 13/6 ,xy=5

\frac{( x + y )}{( x - y )} + \frac{( x - y )}{( x + y )} = \frac{13}{6}, x y = 5

x^2+y^2=2,5yx+y-1=0

x^{2} + y^{2} = 2, 5 y x + y - 1 = 0

x+y=2,x(x-y)=12

x + y = 2, x (x - y) = 12

x^2+y^2=2,6y=3-2x

x^{2} + y^{2} = 2, 6 y = 3 - 2 x

Frequently Asked Questions (FAQ)

What is x/y-y/x = 5/6 ,x^2-y^2=5 ?
The solution to x/y-y/x = 5/6 ,x^2-y^2=5 is