Question

If x=7+4 root 3 ,then find the value of root x +1upon root x

Answer 1

Hi friend✋✋✋✋
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Your answer
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x = 7 + 4√3

$\frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \\ \\ = > \frac{1}{(7 + 4 \sqrt{3} )} \times \frac{(7 - 4 \sqrt{3} )}{(7 - 4 \sqrt{3}) } \\ \\ = > \frac{(7 - 4 \sqrt{3)} }{(7) {}^{2} - (4 \sqrt{3}) {}^{2} } \\ \\ = > \frac{7 - 4 \sqrt{3} }{49 - 48} \\ \\ = > \frac{7 - 4 \sqrt{3} }{1} \\ = > \frac{1}{x} = 7 - 4 \sqrt{3}$
Now,
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$x + \frac{1}{x} = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} \\ \\ = > x + \frac{1}{x} = 14 \\ \\ = > x + \frac{1}{x} + 2 = 14 + 2 (adding \: 2 \: on \: both \: sides) \\ \\ = > ( \sqrt{x} + \frac{1}{ \sqrt{x} } ) {}^{2} = 16 \\ \\ = > \sqrt{x} + \frac{1}{ \sqrt{x} } = \sqrt{16} \\ \\ = > \sqrt{x} + \frac{1}{ \sqrt{x} } = 4$
HOPE IT HELPS

Answer 2

HEYA!!!

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HERE IS YOUR ANSWER...

GIVEN :   x = 7 + 4 (root 3)

TO FIND :   x + 1/x 

SOLUTION :

SINCE,

=> x = 7 + 4 (root 3)

THEREFORE,

=> 1/x = (1) / [7 + 4 (root 3)]

NOW, RATIONALIZING THE DENOMINATOR,

=> 1/x = (1) / [7 + 4 (root 3)] * [7 - 4 (root 3)] / [7 - 4 (root 3)]

=> [7 - 4 (root 3)] / { [7 + 4 (root 3)] * [7 - 4 (root 3)] }

=> [7 - 4 (root 3)] / [49 - 48]

=> [7 - 4 (root 3)] / (1)

THEREFORE,

=> 1/x = [7 - 4 (root 3)] 

THUS,

=> x + 1/x = [7 + 4 (root 3)] + [7 - 4 (root 3)]

=> x + 1/x = 14 

NOW,

ADDING "2" ON BOTH SIDES.

=> x + 1/x + 2 = 14 + 2

=> x + 1/x + 2 = 16

=> [(root x) + (1) / (root x)] ^ 2 = 16

=> (root x) + 1 / (root x) = (root 16)

=> (root x) +1 / (root x) = 4   (ANS)

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HOPE IT HELPS YOU,
THANK YOU.