Đáp án:
1). $A = 5$
2). $A = 3$
Giải thích các bước giải:
Câu 3.
a. $A = \sqrt{\sqrt{3} - \sqrt{6 - 2\sqrt{4 + 2\sqrt{3}}}} + \sqrt{\sqrt{5} + \sqrt{5 + 32\sqrt{69 - 16\sqrt{5}}}}$
$A = \sqrt{\sqrt{3} - \sqrt{6 - 2\sqrt{(\sqrt{3} + 1)^2}}}$ $+ \sqrt{\sqrt{5} + \sqrt{5 + 32\sqrt{(8 - \sqrt{5})^2}}}$
$A = \sqrt{\sqrt{3} - \sqrt{6 - 2(\sqrt{3} + 2)}} + \sqrt{\sqrt{5} + \sqrt{5 + 32(8 - \sqrt{5})}}$
$A = \sqrt{\sqrt{3} - \sqrt{4 - 2\sqrt{3}}}$ $+ \sqrt{\sqrt{5} + \sqrt{261 - 32\sqrt{5}}}$
$A = \sqrt{\sqrt{3} - \sqrt{(\sqrt{3} - 1)^2}} + \sqrt{\sqrt{5} + \sqrt{(16 - \sqrt{5})^2}}$
$A = \sqrt{\sqrt{3} - \sqrt{3} + 1} + \sqrt{\sqrt{5} + 16 - \sqrt{5}}$
$A = \sqrt{1} + \sqrt{16} = 1 + 4 = 5$
2) $A = \sqrt{2\sqrt{5} - \sqrt{25 - 4\sqrt{6 + 2\sqrt{5}}}} + \sqrt{\sqrt{3} + \sqrt{3 + 8\sqrt{7 - 4\sqrt{3}}}}$
$A = \sqrt{2\sqrt{5} - \sqrt{25 - 4\sqrt{(\sqrt{5} + 1)^2}}} + \sqrt{\sqrt{3} + \sqrt{3 + 8\sqrt{(2 - \sqrt{3})^2}}}$
$A = \sqrt{2\sqrt{5} - \sqrt{25 - 4(\sqrt{5} + 1)}} + \sqrt{\sqrt{3} + \sqrt{3 + 8(2 - \sqrt{3})}}$
$A = \sqrt{2\sqrt{5} - \sqrt{21 - 4\sqrt{5}}} + \sqrt{\sqrt{3} + \sqrt{3 + 16 - 8\sqrt{3}}}$
$A = \sqrt{2\sqrt{5} - \sqrt{(2\sqrt{5} - 1)^2}} + \sqrt{\sqrt{3} + \sqrt{(4 - \sqrt{3})^2}}$
$A = \sqrt{2\sqrt{5} - 2\sqrt{5} + 1} + \sqrt{\sqrt{3} + 4 - \sqrt{3}}$
$A = \sqrt{1} + \sqrt{4} = 1 + 2 = 3$
