Question

(2x+3^2=rad(2rad3-5)^2 - rad(2rad3 -4)^2


x=?​

Answer 1

$2x + {3}^{2} = \sqrt{{(2 \sqrt{3} - 5)}^{2}} - \sqrt{ {(2 \sqrt{3} - 4) }^{2} } \\ 2x + 9 = |2 \sqrt{3} - 5 | - |2 \sqrt{3} - 4 | \\ {2 \sqrt{3} }^{2} = 12 \\ 12 < {4}^{2} = 16 \\ 12 < {5}^{2} = 25 \\ = > 2x + 9 = 5 - 2 \sqrt{3} - (4 - 2 \sqrt{3} ) \\ = >2x = 5 - 2 \sqrt{3} - 4 + 2 \sqrt{3} - 9 \\ 2x = - 8 \\ x = - 4$