Question

If√x/y+√y/x=10/3 then find,
1.xy
2.y
​

Answer 1

Answer:

$\frac{ \sqrt{x} }{y} + \frac{ \sqrt{y} }{x} = \frac{10}{3}$

$\frac{x \sqrt{x} + y \sqrt{y} }{xy} = \frac{10}{3}$

Answer 2

Answer:

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

I hope it's your helpful