Math, asked by shuchithamn, 6 months ago

friends answer me this questions
If the answer is correct will mark as brainlist ​

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Answered by aryan073
2

Answer:

Answer ::

Q3)

 \mathfrak{</u><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u><u>}

2x = 3 +  \sqrt{7}

x =  \frac{3 +  \sqrt{7} }{2}

Now put this values in this equation,

\longrightarrow

4 \frac{( 3 + \sqrt{7})^{2}  }{2}  +  \frac{4}{( {3 +  \sqrt{7}) }^{2} }

4( \frac{9 +7 + 6 \sqrt{7})  }{4}  +  \frac{4}{9 + 7 + 6 \sqrt{7} }

16 + 6 \sqrt{7}  +  \frac{4}{16 + 6 \sqrt{7} }

 \frac{256 + 254 + 4}{3 +  \sqrt{7} }

 \frac{514}{3 +  \sqrt{7} }

Q4)

x= \\    \red\bigstar\tt\:  \dfrac {√5-√3}{√5+√3}

y=\\    \red\bigstar\tt\:  \dfrac {√5+√3}{√5-√3}

 {x}^{2}  +  {y}^{2}  =  \: to \: find

 (\frac{ { \sqrt{5}  -  \sqrt{3} })^{2} }{ \sqrt{5} +  \sqrt{3} } ) + (  \frac{ \sqrt{5}  +  \sqrt{3^{2} }  }{ \sqrt{5  -  \sqrt{3} ^{2}  } } )

 \frac{5 - 3 + 2 \sqrt{3} }{5 + 3 + 2 \sqrt{3} } +  \frac{5 + 3 + 2 \sqrt{3} }{5 + 3 - 2 \sqrt{3} }

 \frac{2 + 2 \sqrt{3} }{8 + 2 \sqrt{3} }  +  \frac{8 + 2 \sqrt{3} }{2 + 2 \sqrt{3} }

 \frac{2(2 + 2 \sqrt{3}) + 2 \sqrt{3} (2 + 2 \sqrt{3} ) + 8(8 + 2 \sqrt{3} ) + 2 \sqrt{3} (8 + 2 \sqrt{3})  }{2(8 +  2\sqrt{3} ) + 2 \sqrt{3} (8 +  2\sqrt{3}) }

 \frac{4 + 4 \sqrt{3}  + 4 \sqrt{3} + 12 + 64 + 16 \sqrt{3}  + 16 \sqrt{3}  + 12}{16 +2 \sqrt{3}  + 16 \sqrt{3} + 12  }

 \frac{92 + 40 \sqrt{2} }{28 + 18 \sqrt{3} }

 \frac{2(46 + 20 \sqrt{3}) }{2(14 + 9 \sqrt{3}) }

final \: answer =  \frac{46 + 20{ \sqrt{3} } }{14 + 9 \sqrt{3} }

Q3)

\huge\sf\green{Answer}

solution:

\longrightarrow

 \frac{3  \sqrt{2}  -  2 \sqrt{3}  }{3 \sqrt{2} + 2 \sqrt{3}  }    +   \frac{2 \sqrt{3} }{ \sqrt{3}  -  \sqrt{2} }

 \frac{ \sqrt{3}(3 \sqrt{2}  -  2\sqrt{3}  ) + 2 \sqrt{3}(3   \sqrt{2}  + 2 \sqrt{3}  }{ \sqrt{3}(3 \sqrt{2 } +  2 \sqrt{3} ) -  \sqrt{2}  (3  \sqrt{2} + 2 \sqrt{3}  )}

 \frac{ 3 \sqrt{6}  - 6 \sqrt{6}   + 12 }{3 \sqrt{6} + 6 -   12 - 2 \sqrt{6}  }

 \frac{ - 3 \sqrt{6} + 12 }{ \sqrt{6} - 6 }

 \frac{ - 3 \sqrt{6} + 12 }{ \sqrt{6}  - 6}  \times  -   \frac{3 \sqrt{6} - 12 }{ \sqrt{6}  - 6}

 = 11

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