Question

If x/y in square root +y/x in square root =10/3,then find xy.

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 

Answer 2

Answer:

Step-by-step explanation: