Question

If
$x = \sqrt{5} - 2 \div \sqrt{5} + 2$
Then Find:
${x}^{2}$
Please solve with steps..

Answer 1

x=√5-2/√5+2 ×√5-2/√5-2
x=(5+4-4√5)/5-4
x=(9-4√5)/1
x^2=(9-4√5)^2
x^2=81+80-72√5
x^2=161-72√5

Answer 2

$Given:x = \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 }$

$= \ \textgreater \ \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } * \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2 }$

$= \ \textgreater \ \frac{( \sqrt{5} - 2)^2 }{( \sqrt{5})^2 - (2)^2 }$

$= \ \textgreater \ \frac{5 + 4 - 4 \sqrt{5} }{5 - 4}$

$= \ \textgreater \ \frac{9 - 4 \sqrt{5} }{1}$

$= \ \textgreater \ 9 - 4 \sqrt{5}$


Now,

$x^2 = (9 - 4 \sqrt{5})^2$ 

$= \ \textgreater \ (9)^2 + (4 \sqrt{5} )^2 - 2(9)(4 \sqrt{5})$

$= \ \textgreater \ 81 + 80 - 72 \sqrt{5}$

$= \ \textgreater \ 161 - 72 \sqrt{5}$




Hope this helps!