Question

solve 2/
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Answer 1

Answer:

x = 4 , y = 9

Solution:

Here,

The given equations are ;

2/√x + 3/√y = 2

4/√x - 9/√y = -1

Putting 1/√x = a and 1/√y = b in the given equations wil become as ;

2a + 3b = 2 --------(1)

4a - 9b = -1 --------(2)

Multiplying eq-(1) by 3 , we get ;

=> 3(2a + 3b) = 2•3

=> 6a + 9b = 6 -----------(3)

Now,

Adding eq-(2) and (3) , we get ;

=> 4a - 9b + 6a + 9b = -1 + 6

=> 10a = 5

=> a = 5/10

=> a = 1/2

=> 1/√x = 1/2 { a = 1/√x }

=> √x = 2

=> x = 2²

=> x = 4

Now,

Putting a = 1/2 in eq-(1) , we get ;

=> 2a + 3b = 2

=> 2•(1/2) + 3b = 2

=> 1 + 3b = 2

=> 3b = 2 - 1

=> 3b = 1

=> b = 1/3

=> 1/√y = 1/3 { b = 1/√y }

=> √y = 3

=> y = 3²

=> y = 9

Hence ,

x = 4 , y = 9

Answer 2

${\bold{\huge{\textbf{given question:}}}}$

${\frac{2}{\sqrt{x}}+ \frac{3}{\sqrt {y}}=2 \rightarrow(1)}$

${\frac{4}{\sqrt{x}}- \frac{9}{\sqrt{y}}=-1 \rightarrow(2)}$

${\bold{\underline{\large{\red{\textbf{Answer:}}}}}}$

let u = ${\frac{1}{\sqrt{x}}}$ and v= ${\frac{1}{\sqrt{y}}}$

so the equation (1) and (2) will be:

${\bold{\pink{2u + 3v = 2}}}\rightarrow(3)$

${\bold{\pink{4u -9v =-1}}}\rightarrow(4)$

now multiply equation (3) by 2:

${\bold{4u + 6v = 4}}\rightarrow(5)$

now by elimination method in equation (4) and (5)

we get,

${\bold{v= \frac{1}{3}}}$

and put the value of v in equation (4) we get,

${\bold{u= \frac{1}{2}}}$

now for the values of x and y:

$\frac{1}{\sqrt{x}}= u = \frac{1}{3}$

${\boxed{\red{x = 9}}}$

and

$\frac{1}{\sqrt{y}}= u = \frac{1}{2}$

${\boxed{\red{y = 4}}}$