Question

x^2 − x(√7−2) − 2√7 = 0

Answer 1

$x^2-x( \sqrt{7}-2)-2 \sqrt{7}=0\\D=(-( \sqrt{7}-2))^2-4*1*(-2 \sqrt{7})=\\=( \sqrt{7}-2)^2+8 \sqrt{7}=( \sqrt{7})^2-4 \sqrt{7}+4+8 \sqrt{7}=\\=7+4 \sqrt{7}+4=11+4 \sqrt{7}\\\\x_{1,2}= \frac{ \sqrt{7}-2 б \sqrt{11+4 \sqrt{7} } }{2*1}= \frac{ \sqrt{7}-2б \sqrt{2^2+2*2 \sqrt{7}+( \sqrt{7})^2 } }{2}=\\\\= \frac{ \sqrt{7}-2б \sqrt{(2+ \sqrt{7} )^2} }{2}= \frac{ \sqrt{7} -2б|2+ \sqrt{7}|} {2}$
$x_1= \frac{ \sqrt{7}-2+2+ \sqrt{7} }{2}= \frac{2 \sqrt{7} }{2} = \sqrt{7}\\\\x_2=\frac{ \sqrt{7}-2-2- \sqrt{7} }{2}= \frac{-4}{2}=-2$