# If √(x/y) = 10/3 – √(y/X) and x – y = 8, then the value of xy is equal to :

(a) 36

(b) 24

(c) 16

(d) 9

**Answer: (d) 9
**

**Solution:-**

√(x/y) = 10/3 – √(y/x)

√(x/y) + √(y/x) = 10/3

(x + y)/√xy = 10/3

Square on both side,

(x + y)²/xy = 100/9

(x² + y² + 2 xy)/xy = 100/9

By cross multiplication,

9 (x² + y²) + 18 xy = 100 xy

9 (x² + y²) = 100 xy – 18 xy

9 (x² + y²) = 82 xy …………………….. (1)

x – y = 8

Square on both side,

(x – y)² = 64

x² + y² – 2 xy = 64

x² + y² = 64 + 2 xy

Put the value of x² + y² = 64 + 2 xy in equation (1),

Then, 9 (64 + 2 xy) = 82 xy

9 x 64 + 18 xy = 82 xy

9 x 64 = 82 xy – 18 xy

9 x 64 = 64 xy

xy = 9 x 64/64

xy = 9

Then, the value of xy is 9.

Hence, the correct answer is option (d) 9.