Question Number 139468 by mathdanisur last updated on 27/Apr/21
$${prove}:\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}}\:=\:\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$
Answered by OlafThorendsen last updated on 27/Apr/21
$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)} \\ $$$${x}\:=\:\:\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$
Commented by mathdanisur last updated on 02/May/21
$${thanks}\:{sir} \\ $$