Question

опишите подробно решение
$\sqrt{9 - 2 \sqrt{20 } } - \sqrt{9 + 2 \sqrt{20} }$

Answer 1

$\sqrt{9-2 \sqrt{20} } - \sqrt{9+2 \sqrt{20} }=\\\\= \sqrt{9-2 \sqrt{4*5} }- \sqrt{9+2\sqrt{4*5} }=\\\\= \sqrt{9-2*2 \sqrt{5} }- \sqrt{9+2*2 \sqrt{5} }=\\\\= \sqrt{2^2-2*2 \sqrt{5}+( \sqrt{5})^2 }- \sqrt{2^2+2*2 \sqrt{5}+( \sqrt{5})^2 }=\\\\= \sqrt{(2- \sqrt{5})^2 } - \sqrt{(2+ \sqrt{5})^2 }=\\\\=|2- \sqrt{5}|-|2+ \sqrt{5}|=-(2- \sqrt{5})-(2+ \sqrt{5})=\\\\=-2+ \sqrt{5}-2- \sqrt{5}=-4$

Answer 2

$x=\sqrt{9-\sqrt{80}}-\sqrt{9+\sqrt{80}}\ \textless \ 0;$

$x^2=9-\sqrt{80}+9+\sqrt{80}-2\sqrt{(9-\sqrt{80})(9+\sqrt{80})}=18-2\sqrt{81-80}=$

$=18-2=16;\ x=\pm 4; x\ \textless \ 0\Rightarrow x=-4$

Ответ:- 4