Question

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

, then find xy.
[Hint. Square both the sides]
​

Answer 1

Step-by-step explanation:

squaring on both side

x/y+y/x+2=100/9

x/y+y/x=100/9-2

x^2+y^2/xy=100-18/9

×^2+y^2=82/9×y

9x^2+9y^2=82xy

9x^2+9y^2-82xy=0

9x^2-81xy-×y+9y^2=0

9x(x-9y)-y(x-9y)=0

(9x-y) (x-9y)=0

x=9y

y=9x

9y=81x

9y=×

x=0 ,y=0