x-7-4-3-thenx-1-x-

Question Number 27525 by sirigidiravikumar@gmail.com last updated on 08/Jan/18

x = 7 \times 4 \sqrt{3} t h e n x + 1 / x = ?

Commented by Rasheed.Sindhi last updated on 09/Jan/18

May be x = 7 + 4 \sqrt{3}

(Mistakenly written as x = 7 \times 4 \sqrt{3})

If x = 7 + 4 \sqrt{3}

x + \frac{1}{x} = (7 + 4 \sqrt{3}) + \frac{1}{7 + 4 \sqrt{3}}

= (7 + 4 \sqrt{3}) + \frac{1}{7 + 4 \sqrt{3}} \times \frac{7 - 4 \sqrt{3}}{7 - 4 \sqrt{3}}

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

= 7 + 4 \sqrt{3} + \frac{7 - 4 \sqrt{3}}{49 - 48}

= 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3}

= 14

Answered by Joel578 last updated on 09/Jan/18

x = 7 . 4 \sqrt{3} = 28 \sqrt{3}

x + \frac{1}{x} = 28 \sqrt{3} + \frac{1}{28 \sqrt{3}} = \frac{2353 \sqrt{3}}{84} \approx 48.52

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