\frac{5 +  \sqrt{11} }{3 - 2 \sqrt{11} }  = x + y \sqrt{11}
Find the value of ‘x’ and ‘y’​

Question

 \frac{5 +  \sqrt{11} }{3 - 2 \sqrt{11} }  = x + y \sqrt{11}
Find the value of ‘x’ and ‘y’​

in progress 0
Anna 4 months 2021-07-17T11:59:19+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-17T12:00:27+00:00

    Answer:

    3−2

    11

    5+

    11

    =x+y

    11

    To Find:

    Find the value of x and y

    Solution:

    \begin{gathered} \implies \tt \bold{ \frac{5 + \sqrt{11} }{3 – 2 \sqrt{11} } = x + y \sqrt{11} } \\ \end{gathered}

    3−2

    11

    5+

    11

    =x+y

    11

    Rewrite the LHS and RHS .

    \begin{gathered}\implies \tt \bold{ x + y \sqrt{11} = \frac{5 + \sqrt{11} }{3 – 2 \sqrt{11} } } \\ \end{gathered}

    ⟹x+y

    11

    =

    3−2

    11

    5+

    11

    Now , Rationalize the denominator by 3+2√11

    \begin{gathered}\implies \tt \bold{ x + y \sqrt{11} = \frac{5 + \sqrt{11} }{3 – 2 \sqrt{11}} } \bold{ \times \frac{3 + 2 \sqrt{11} }{3 + 2 \sqrt{11} }} \\ \end{gathered}

    ⟹x+y

    11

    =

    3−2

    11

    5+

    11

    ×

    3+2

    11

    3+2

    11

    Simplify the RHS

    By using the formula a²-b²=(a+b)(a-b)

    \begin{gathered}\implies \tt \bold{ x + y \sqrt{11} = \frac{(5 + \sqrt{11})(3 + 2 \sqrt{11}) }{ {3}^{2} – 4(11)} } \\ \end{gathered}

    ⟹x+y

    11

    =

    3

    2

    −4(11)

    (5+

    11

    )(3+2

    11

    )

    \begin{gathered}\implies \tt \bold{ x + y \sqrt{11} = \frac{15 + 13 \sqrt{11} + 22 }{ – 35} } \\ \end{gathered}

    ⟹x+y

    11

    =

    −35

    15+13

    11

    +22

    Adding the numbers 15 and 22 is 37 .

    \begin{gathered}\implies \tt \bold{ x + y \sqrt{11} = \frac{37 + 13 \sqrt{11} }{ – 35}} \\ \end{gathered}

    ⟹x+y

    11

    =

    −35

    37+13

    11

    Now , the comparing the LHS AND RHS.

    \begin{gathered}\implies \tt \bold{ x + y \sqrt{11} = \frac{ – 37}{35} – \frac{13}{35} \sqrt{11}} \\ \end{gathered}

    ⟹x+y

    11

    =

    35

    −37

    35

    13

    11

    \therefore \boxed{ \bf{ \red{x = \frac{ – 37}{35}}} }∴

    x=

    35

    −37

    \therefore \boxed{ \red{ \bf{y = \frac{ – 13}{35}}}}∴

    y=

    35

    −13

    H

    Step-by-step explanation:

    please mark me as brainlist

    0
    2021-07-17T12:00:29+00:00

    Step-by-step explanation:

     \huge \textbf{ \underline{Answer :-}}

    Given :

    •  \frac{5 + \sqrt{11} }{3 - 2 \sqrt{11} } = x + y \sqrt{11}

    To Find:

    • Find the value of x and y

    Solution:

     \implies \tt \bold{ \frac{5 +  \sqrt{11} }{3 - 2 \sqrt{11} }  = x + y \sqrt{11} } \\

    Rewrite the LHS and RHS .

    \implies \tt \bold{ x + y \sqrt{11}  =  \frac{5 +  \sqrt{11} }{3 - 2 \sqrt{11} } } \\

    Now , Rationalize the denominator by 3+211

    \implies \tt \bold{ x + y \sqrt{11}  =  \frac{5 +  \sqrt{11} }{3 - 2 \sqrt{11}} } \bold{  \times  \frac{3 + 2 \sqrt{11} }{3 + 2 \sqrt{11} }}  \\

    Simplify the RHS

    By using the formula a²-b²=(a+b)(a-b)

    \implies \tt \bold{ x + y \sqrt{11}  =  \frac{(5 +  \sqrt{11})(3 + 2 \sqrt{11})  }{ {3}^{2} - 4(11)} }  \\

    \implies \tt \bold{ x + y \sqrt{11}  =  \frac{15 + 13 \sqrt{11} + 22 }{ - 35} } \\

    Adding the numbers 15 and 22 is 37 .

    \implies \tt \bold{ x + y \sqrt{11}  =  \frac{37 + 13 \sqrt{11} }{ - 35}}  \\

    Now , the comparing the LHS AND RHS.

    \implies \tt \bold{ x + y \sqrt{11}  =  \frac{ - 37}{35}  -  \frac{13}{35}  \sqrt{11}}  \\

     \therefore \boxed{ \bf{ \red{x =  \frac{ - 37}{35}}} }

     \therefore \boxed{ \red{ \bf{y =  \frac{ - 13}{35}}}}

    Hope it will help you mate !!

    Mark as Brainlist !!

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