Question

if
$x = 7 + 4 \sqrt{3 \: }$
Then find the value of
$x + \frac{1}{x}$
​

Answer 1

Answer: 14

Step by step explanation:

x = 7 + 4√3 .. (1)

» 1/x = 1/( 7 + 4√3 )

Rationalizing the denominator,

1/x = ( 7 - 4√3 ) / ( 7 + 4√3 )( 7 - 4√3 )

= ( 7 - 4√3 ) / [ 7² - ( 4√3 )² ]

= ( 7 - 4√3 ) / [ 49 - 48 ]

= ( 7 - 4√3)

.°. 1/x = 7 - 4√3 .. (2)

Therefore ,

x + 1/x = (7 + 4√3) + (7 - 4√3)

x + 1/x = 7 + 7

x + 1/x = 14

Answer 2

SOLUTION:-

Given:

x= 7 + 4√3

To find:

The value of x+ 1/x.

Explanation:

We have,

x= 7+4√3

&

1/x = 1/ 7+4√3

Rationalising:

$= > \frac{1 \times( 7 - 4 \sqrt{3}) }{7 + 4 \sqrt{3} \times (7 - 4 \sqrt{3}) } \\ \\ = > \frac{7 -4 \sqrt{3} }{ ({7)}^{2} - ( {4 \sqrt{3} )}^{2} } \\ \\ = > \frac{7 - 4 \sqrt{3} }{49 - 16 \times 3} \\ \\ = > \frac{7 - 4 \sqrt{3} }{49 - 48} \\ \\ = > \frac{7 - 4 \sqrt{3} }{1} \\ \\ = > \frac{1}{x} = 7 - 4 \sqrt{3}$

Now,

=) x+ 1/x = 7+ 4√3 + 7-4√3

=) x + 1/x = 7 +7

=) x+ 1/x = 14.

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