Question

if x
$= \sqrt{5} + 2$
then
x + 1/x = ??​

Answer 1

Answer:

$2 \sqrt{5}$

Step by step solution:

Give,

$x = \sqrt{5} + 2$

To find,

$x + \frac{1}{x}$

Now,

Put the value of X,

we get,

$\sqrt{5} +2 + \frac{1}{ \sqrt{5} + 2 }$

$\sqrt{5} + 2 + \frac{ \sqrt{5} - 2}{( \sqrt{5} + 2)( \sqrt{5} - 2) }$

$\sqrt{5} + 2 + \frac{ \sqrt{5} - 2}{ { \sqrt{5} }^{2} - {2}^{2} }$

Because,

${a}^{2} - {b}^{2} = (a + b)(a - b)$

${ \sqrt{5} }^{2} - {2}^{2} = 5 - 4 = 1$

Continue,

$\sqrt{5} + 2 + \sqrt{5} - 2 = 2 \sqrt{5}$