Prove-that-13x-x-2-13x-1-13-if-x-13-2-3-

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

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

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

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

x = \sqrt{13} + 2 \sqrt{3}