Question

If x=7-4√3 then the value of (x+1/x)

Answer 1

$x \: = \: 7 \: - \: 4 \sqrt{3}$

___________ [ GIVEN ]

• We have to find the value of $x \: + \: \dfrac{1}{x}$

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We have ..

=> $x \: = \: 7 \: - \: 4 \sqrt{3}$

Now,

=> $\dfrac{1}{x} \: = \: \dfrac{1}{7 \: - \: 4 \sqrt{3} }$

Rationalize it

=> $\dfrac{1}{x} \: = \: \dfrac{1}{7 \: - \: 4 \sqrt{3} } \: \times \: \dfrac{7 \: + \: 4 \sqrt{3} }{7 \: + \: 4 \sqrt{3} }$

=> $\dfrac{1}{x} \: = \: \dfrac{7 \: + \: 4 \sqrt{3} }{(7 \: + \: 4 \sqrt{3} )(7 \: - \: 4 \sqrt{3} )}$

(a + b) (a - b) = a² - b²

=> $\dfrac{1}{x} \: = \: \dfrac{7 \: + \: 4 \sqrt{3} }{(7 )^{2} \: - \: (4 \sqrt{3} ) ^{2} }$

=> $\dfrac{1}{x} \: = \: \dfrac{7 \: + \: 4 \sqrt{3} }{49\: - \: 48 }$

=> $\dfrac{1}{x} \: = \: \dfrac{7 \: + \: 4 \sqrt{3} }{ 1 }$

=> $\dfrac{1}{x} \: =\:7 \: + \: 4 \sqrt{3}$

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$x \: + \: \dfrac{1}{x}$

Put the known values above

=> $7 \: - \: 4 \sqrt{3}$ + $7 \: + \: 4 \sqrt{3}$

=> $14$

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$x \: + \: \dfrac{1}{x}$ = $14$

_______________ [ ANSWER ]

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