Question

if x =√13 + 2√3, find the value of x-1/x

Answer 1

Hello Mate!

$x = \sqrt{13} + 2 \sqrt{3} \\ \frac{1}{x} = \frac{1}{ \sqrt{13} + 2 \sqrt{3} } \times \frac{ \sqrt{13} - 2 \sqrt{3} }{ \sqrt{13} - 2 \sqrt{3} } \\ = \frac{ \sqrt{13} - 2 \sqrt{3} }{13 - 12} \\ = \sqrt{13} - 2 \sqrt{3} \\ \sqrt{13} + 2 \sqrt{3} - ( \sqrt{13} - 2 \sqrt{3} ) \\ = 4 \sqrt{3}$

Hope it helps☺!✌

Answer 2

Answer:

$4\sqrt{3}$

Step-by-step explanation:

Given,

x = √13 + 2√3,

$\implies \frac{1}{x}=\frac{1}{\sqrt{13}+2\sqrt{3}}$

$=\frac{1}{\sqrt{13}+2\sqrt{3}}\times \frac{\sqrt{13}-2\sqrt{3}}{\sqrt{13}-2\sqrt{3}}$

$=\frac{\sqrt{13}-2\sqrt{3}}{(\sqrt{13})^2-(2\sqrt{3})^2}$

$=\frac{\sqrt{13}-2\sqrt{3}}{13-12}$

$=\frac{\sqrt{13}-2\sqrt{3}}{1}$

$=\sqrt{13}-2\sqrt{3}$

Thus,

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

$=\sqrt{13}+2\sqrt{3}-\sqrt{13}+2\sqrt{3}$

$=4\sqrt{3}$