Math, asked by varshasen18, 5 months ago

answer this question on time​

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Answered by gujjuak
1

Answer:

your first answer is in the image

and your second answer is 6 -2√5

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Answered by rohitkhajuria90
1

(a)

 \frac{4 + 3 \sqrt{5} }{3 +  \sqrt{5} }  -  \frac{4  -  3 \sqrt{5} }{3  -   \sqrt{5} } \\  =  \frac{(4 + 3 \sqrt{5})(3 -  \sqrt{5}) - (4 - 3 \sqrt{5} )(3 +  \sqrt{5}) }{ {3}^{2} -  { ( \sqrt{5} )}^{2}  }  \\  =  \frac{12 - 4 \sqrt{5} + 9 \sqrt{5}  - 75 - 12 - 4 \sqrt{5}  + 9 \sqrt{5}   + 75}{9 - 5}  \\  =  \frac{ - 8 \sqrt{5} + 18 \sqrt{5}  }{4}  \\  =  \frac{10 \sqrt{5} }{4}  \\  =  \frac{5 \sqrt{5} }{2}

(b)

x =  \frac{1}{2 +  \sqrt{5} }  \\  \\  {x}^{2}  + 4x + 1 \\  \\  { (\frac{1}{2 +  \sqrt{5} }) }^{2}  + 4(2 +  \sqrt{5)}  + 1 \\  \\  =  \frac{1}{4 + 5 + 4 \sqrt{5} }  + 8 + 4 \sqrt{5}  + 1 \\  \\  =  \frac{1}{9 + 4 \sqrt{5} }  + 4 \sqrt{5}  + 9 \\  \\  =  \frac{1 +   {(9 + 4 \sqrt{5})}^{2}  }{9 + 4 \sqrt{5} }  \\  \\  =  \frac{1 + 81 + 80 + 72 \sqrt{5} }{9 + 4 \sqrt{5} }  \\  \\  =  \frac{162 + 72 \sqrt{5} }{9 + 4 \sqrt{5} }  \\  \\  =  \frac{18(9 + 4 \sqrt{5}) }{9 + 4 \sqrt{5} }  \\  \\  = 18

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