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

$$x=7\times 4\sqrt{3}thenx+1/x=?$$

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

$$\mathrm{May}\mathrm{be}x=7+4\sqrt{3}$$$$(\mathrm{Mistakenly}\mathrm{written}\mathrm{as}x=7\times 4\sqrt{3})$$$$\mathrm{If}\mathrm{x}=7+4\sqrt{3}$$$$\mathrm{x}+\frac{1}{\mathrm{x}}=(7+4\sqrt{3})+\frac{1}{7+4\sqrt{3}}$$$$=(7+4\sqrt{3})+\frac{1}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7-4\sqrt{3}}$$$$=(7+4\sqrt{3})+\frac{7-4\sqrt{3}}{{\left(7\right)}^2-{\left(4\sqrt{3}\right)}^2}$$$$=7+4\sqrt{3}+\frac{7-4\sqrt{3}}{49-48}$$$$=7+4\sqrt{3}+7-4\sqrt{3}$$$$=14$$

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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