Question

plz answer this question​

Answer 1

$\rm :\implies\:2x = \sqrt{5} + 1$

$\rm :\implies\:2x - 1 = \sqrt{5}$

On squaring, both sides we get

$\rm :\implies\: {(2x - 1)}^{2} = {( \sqrt{5}) }^{2}$

$\rm :\implies\: {4x}^{2} + 1 - 4x = 5$

$\rm :\implies\: {4x}^{2} + 1 - 4x - 5 = 0$

$\rm :\implies\: {4x}^{2} - 4x - 4 = 0$

$\rm :\implies\:4( {x}^{2} - x - 1) = 0$

$\rm :\implies\: {x}^{2} - x - 1 = 0$

$\large{\boxed{\boxed{\bf{Hence, Proved}}}}$