Đáp án:
`a)` `A=2`
`b)` `A=-6\sqrt{7}`
Giải thích các bước giải:
`a)` `A=\sqrt{6-2\sqrt{5}}+\sqrt{14-6\sqrt{5}}`
`=\sqrt{5-2\sqrt{5}.1+1^2}+\sqrt{3^2-2.2.\sqrt{5}+5}`
`=\sqrt{(\sqrt{5}-1)^2}+\sqrt{(3-\sqrt{5})^2}`
`=|\sqrt{5}-1|+|3-\sqrt{5}|`
`=\sqrt{5}-1+3-\sqrt{5}=2`
Vậy `A=2`
$\\$
`b)` `A=\sqrt{127-48\sqrt{7}}-\sqrt{127+48\sqrt{7}}`
`=\sqrt{64-48\sqrt{7}+63}-\sqrt{64+48\sqrt{7}+63}`
`=\sqrt{8^2-2.8.3\sqrt{7}+(3\sqrt{7})^2}-\sqrt{8^2+2.8.3\sqrt{7}+(3\sqrt{7})^2}`
`=\sqrt{(8-3\sqrt{7})^2}-\sqrt{(8+3\sqrt{7})^2}`
`=|8-3\sqrt{7}|-|8+3\sqrt{7}|`
`=8-3\sqrt{7}-8-3\sqrt{7}=-6\sqrt{7}`
Vậy `A=-6\sqrt{7}`
