Question

please solve this question

Answer 1

Square both sides: 

x/y + 2 + y/x = 100/9 

Subtract 2 from both sides: 

x/y + y/x = 82/9 

Combine the fractions: 

(x^2 + y^2) / xy = 82/9 

From here by inspection, we can see that at least two solutions are (1, 9) and (9, 1) making xy = 9. But we will continue by factoring: 

9x^2 + 9y^2 = 82xy 

9x^2 - 82xy + 9y^2 = 0 

9x^2 - 81xy - xy + 9y^2 = 0 

9x(x - 9y) - y(x - 9y) = 0 

(9x - y)(x - 9y) = 0 

x = 9y OR y = 9x 

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