Question

if
$\sqrt{ \frac{x}{y } } + \sqrt{ \frac{y}{x} } = \frac{10}{3}$
then find the value of xy.

Answer 1

★ QUADRATIC RESOLUTION ★

☣ √x/y + √y/x = 10/3

☣ x + y / √xy = 10/3

☣ x + y = 10 ; xy = 9

☣ y = 9/x ... ( i )

substituting ( i ) in previous equation -

☣ x + 9/x = 10

☣ x² - 10x + 9 = 0

☣ x² - 9x - 1x + 9 = 0

☣ x ( x - 9 ) -1 ( x - 9 ) = 0

☣ ( x - 1 ) ( x - 9 ) = 0

☣ x = 1 , x = 9

☣ If x = 1 ; y = 9
☣ If x = 9 ; y = 1

In overall dimensions ,

☣ xy = 9

and above obtained values satisfy the quadratic equation given above

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