Question

x is equal to root 3 + 1 upon 2 write in the form of 4 x cube + 2 x square - 8 x + 7

Answer 1

$HeyThere$ !!

$Given,$$x = \frac{ \sqrt{3 } + 1 }{2}$

$Now,$
$4 {x}^{3} + 2 {x}^{2} - 8x + 7$
$substituting \: x' s \: value \:$
$4( \frac{ \sqrt{3} + 1 }{2} ) {}^{3} + 2( \frac{ \sqrt{3} + 1 }{2}) {}^{2} - 8( \frac{ \sqrt{3} + 1 }{2} + 7$
$= 2(3 \sqrt{3} + 9 + 3 \sqrt{3} + 1) + ( 3 + 2 \sqrt{3} + 1) - 4( \sqrt{3} + 1) + 7$
$= (6 \sqrt{3} + 10) + (2 \sqrt{3} + 4) - 4 \sqrt{3} + 4 + 7$
$= 6 \sqrt{3} + 2 \sqrt{3} - 4 \sqrt{3} + 10 + 4 + 4 + 7$
$= 4 \sqrt{3} + 25$

$Hope \: my \: ans.'s \: satisfactory.$ !!