Solve : - 2/√3 + 3/√y = 2; 4/√x. 9/√y = 1.

Question

Solve : - \(\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2;\frac{4}{\sqrt{x}}.\frac{9}{\sqrt{y}}=-1\).

Answer 1

Let 1/√x be ‘m’ and 1/√y be ‘n’,

Then the given equations become 

2m + 3n = 2 

4m - 9n = -1

( 2m + 3n = 2) X - 2 

⇒ − 4m − 6n = − 4 …(1) 

4m - 9n = -1 

4m − 9n = − 1 …(2)

Adding (1) and (2)

We get −15n = − 5 ⇒ n = 1/3

Substituting n = 1/3 in 2m + 3n = 2, we get