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Question Number 173888 by azadsir last updated on 20/Jul/22

$$\mathrm{Prove}\mathrm{that},\frac{13\mathrm{x}}{{\mathrm{x}}^2-\sqrt{13\mathrm{x}}+1}=\sqrt{13}\mathrm{if},\mathrm{x}=\sqrt{13}+2\sqrt{3}$$

Answered by a.lgnaoui last updated on 20/Jul/22

$$$$$$\frac{13x}{(x^2-\sqrt{13}x+1)}=\frac{13x}{\sqrt{13}x}\Rightarrow x^2-\sqrt{13}x+1=\sqrt{13}x$$$$x^2-2\sqrt{13}x+1=0\Rightarrow {(x-\sqrt{13})}^2-{\left(2\sqrt{3}\right)}^2=0$$$$x=\sqrt{13}+2\sqrt{3}$$

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