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X/y+y/x=10/3; x^2-y^2=72

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The solution

You have entered [src]
x   y       
- + - = 10/3
y   x       
$$\frac{x}{y} + \frac{y}{x} = \frac{10}{3}$$
 2    2     
x  - y  = 72
$$x^{2} - y^{2} = 72$$
x^2 - y^2 = 72
Rapid solution
$$x_{1} = -9$$
=
$$-9$$
=
-9

$$y_{1} = -3$$
=
$$-3$$
=
-3
$$x_{2} = 9$$
=
$$9$$
=
9

$$y_{2} = 3$$
=
$$3$$
=
3
$$x_{3} = - 3 i$$
=
$$- 3 i$$
=
-3*i

$$y_{3} = - 9 i$$
=
$$- 9 i$$
=
-9*i
$$x_{4} = 3 i$$
=
$$3 i$$
=
3*i

$$y_{4} = 9 i$$
=
$$9 i$$
=
9*i
Numerical answer [src]
x1 = -9.0
y1 = -3.0
x1 = -9.0
y1 = -3.0