Math, asked by jaysingh70, 2 months ago

plz ans rhe question ​

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Answered by abhishekpaul9510
0

Answer:

Hope this is OK for you completely

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Answered by 12thpáìn
3

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
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