Question

plz ans rhe question ​

Answer 1

Answer:

Hope this is OK for you completely

Answer 2

Given

• ${ \sf \: \dfrac{2}{ \sqrt{x} } + \dfrac{3}{ \sqrt{y} } = 2 }$
• ${ \sf \dfrac{4}{ \sqrt{x} } - \dfrac{9}{ \sqrt{y} } = - 1}$

To Find

• Value of x and y

let

$\pink{\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c | } \qquad&\qquad \\ \sf{a = \dfrac{1}{\sqrt{x}}} & \sf b = \dfrac{1}{ \sqrt{y} } \\ \\ \end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}}$

Now

$\sf{2a + 3b = 2 \: \: \: \: \: \: - - - - - (1)}$

${ \sf 4a - 9b = - 1 \: \: \: \: \: - - - - - (2)}$

• On solving Equation 1 we get

$\sf{ \: \: \: \: \: : \: \: \implies 2a + 3b = 2 }$

• Subtracting both sides by 3b

$\sf{ \: \: \: \: \: : \: \: \implies 2a + 3b - 3b = 2 - 3b }$

$\sf{ \: \: \: \: \: : \: \: \implies 2a= 2 - 3b }$

• Diving both sides by 2

$\sf{ \: \: \: \: \: : \: \: \implies \dfrac{2a}{2} = \dfrac{2 - 3b}{2} }$

$\sf{ \: \: \: \: \: : \: \: \implies \gray{a= \dfrac{2 - 3b}{2} } \: \: \: \: \: \: \: \: \: \: \: \: - - - - \: \: \: (3)}$

On Substituting the Value of a in Equation 2

we get

$\sf{ \: \: \: \: \: : \: \: \implies 4 \left( \dfrac{2 - 3b}{2} \right) - 9b = - 1}$

$\sf{ \: \: \: \: \: : \: \: \implies \dfrac{8 - 12b}{2} - 9b = - 1}$

• Taking LCM of 2 and 1

$\sf{ \: \: \: \: \: : \: \: \implies \dfrac{8 - 12b - 18b}{2} = - 1}$

• Multiplying both sides by 2

$\sf{ \: \: \: \: \: : \: \: \implies \dfrac{8 - 30b}{2} \times 2 = - 1 \times 2}$

$\sf{ \: \: \: \: \: : \: \: \implies 8 - 30b = - 2}$

• Subtracting both sides by 8

$\sf{ \: \: \: \: \: : \: \: \implies 8 - 8- 30b = - 2 - 8}$

$\sf{ \: \: \: \: \: : \: \: \implies - 30b = - 10}$

• Diving both sides by -30

$\sf{ \: \: \: \: \: : \: \: \implies \dfrac{ - 30b}{ - 30} = \dfrac{ - 10}{ - 30} }$

$\sf{ \: \: \: \: \: : \: \: \implies b = \dfrac{ 1}{ 3} }$

Putting the Value of b in Equation 3

$\sf{ \: \: \: \: \: : \: \: \implies {a= \dfrac{2 - 3 \times \dfrac{1}{3} }{2} } }$

$\sf{ \: \: \: \: \: : \: \: \implies {a= \dfrac{2 - 1 }{2} } }$

$\sf{ \: \: \: \: \: : \: \: \implies {a= \dfrac{1 }{2} } }$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c | } \qquad&\qquad \\ \sf{a = \dfrac{1}{2} = \dfrac{1}{\sqrt{x}}} & \sf b = \dfrac{1}{3} = \dfrac{1}{ \sqrt{y} } \\ \\ \sf \sqrt{x} = 2& \sf \sqrt{y} = 3 \\ \\ \sf x = {2}^{2} & \sf y = {3}^{2} \\ \\ \hline \sf x = 4 & \sf y = 9\end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

• Hance the Value of x is 4 and y is 9