Question

√x/y+√y/x=10/3 find then xy​

Answer 1

Step-by-step explanation:

Given :-

√(x/y) +√(y/x) = 10/3

To find :-

Find the value of xy ?

Solution :-

Given that

√(x/y) +√(y/x) = 10/3

We know that

√(a/b) = √a / √b

Therefore,

√(x/y) +√(y/x) = 10/3

=> (√x/√y) + (√y/√x) = 10/3

=> [(√x×√x) +(√y×√y)]/(√y×√x) = 10/3

=> [(√x)²+(√y)²]/√(yx) = 10/3

=> (x+y)/√(xy) = 10/3

On squaring both sides then

=> [(x+y)/√(xy)]²= (10/3)²

=> (x+y)²/(xy) = 100/9

=> (x+y)²/(xy) = 10²/9

It can be written as

=> (x+y)²/(xy) = (9+1)²/(9×1) or (1+9)²/(1×9)

On comparing both sides

We get , the values of x and y are 9 and 1 or 1 and 9

So,

The value of xy = 9×1 or 1×9 = 9

Answer:-

The value of xy for the given problem is 9

Used formulae:-

→ √(a/b) = √a / √b

→ √(ab) = √a × √b