Math, asked by Hkamboj, 1 year ago

please solve it imidiately please I request

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Answers

Answered by MsQueen
3
 \textbf{Solution:}
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1) Represent 0.235 bar in the p/q form.

Let x = 0.235235......(1)

1000x = 235.235235.......(2)

On subtracting (1) from (2) we get;

1000x - x = 235 - 0

=> 999x = 235

=> x =  \frac{235}{999}

Hence, it is in p/q form.

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2) Represent 0. 2113 bar on 3 in p/q form.

Let x = 0.2113333....(1)

100x = 211.33333....(2)

1000x = 2113.33333......(3)

On subtracting (2) from (3) we get;

1000x - 100x = 2113 - 211

=> 900x = 1902

=> x =  \frac{1902}{900}

Hence, it is in the P / Q form.

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3)

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

Hence, √7 - √3 is the answer.

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4)
 \frac{4}{3 -  \sqrt{5} }  \\  \\ \frac{4}{3 -  \sqrt{5} }  \times  \frac{3 +  \sqrt{5} }{3 +  \sqrt{5} }  \\  \\  \frac{4(3 +  \sqrt{5}) }{(3) {}^{2} -  ( \sqrt{5} ) {}^{2} }  \\  \\  \frac{4(3 +  \sqrt{5}) }{4}  = 3 +  \sqrt{5}

Therefore, the value of 0 + 4/a , is..

 \frac{4}{3 +  \sqrt{5} }  \\ \\   \frac{4}{3 +  \sqrt{5} }  \times  \frac{3 -  \sqrt{5} }{3 -  \sqrt{5} }  \\  \\  \frac{4(3 -  \sqrt{5} )}{(3) {}^{2}  - ( \sqrt{5} ) {}^{2} }  \\  \\  \frac{4(3 -  \sqrt{5}) }{4}  = 3 -  \sqrt{5}


Hence, the value is ( 3 - √5 ).

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#thank you!! ☺☺

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