Question

√(4-2√3)+√(4+2√3)la puterea a Va rog aratati-mi si calculele.

Answer 1

$\sqrt{4-2\sqrt{3}} = \sqrt{(\sqrt{3}-\sqrt{1})^2} = \sqrt{3} - \sqrt{1}$
$\sqrt{4+2\sqrt{3}} = \sqrt{(\sqrt{3}+\sqrt{1})^2} = \sqrt{3} + \sqrt{1}$
Din cele de mai sus rezultă:
$( \sqrt{4-2\sqrt{3}} + \sqrt{4+2\sqrt{3}})^5 = (\sqrt{(\sqrt{3}-\sqrt{1})^2} + \sqrt{(\sqrt{3}+\sqrt{1})^2})^5$
$\sqrt{3} - \sqrt{1} + \sqrt{3} + \sqrt{1} = 2\sqrt{3}$
$(2\sqrt{3})^5 = 2^5*\sqrt{3}^5 = 32*9*\sqrt{3} = 288\sqrt{3}$