Rút gọn a) √9- √17 – √9+ √17 b) √11-2√30 + √13+2√42 mình cần gấp cảm ơn mn hứa 5* và TLHN.

Đáp án:

`a)` `\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}=-\sqrt{2}`

`b)` `\sqrt{11-2\sqrt{30}}+\sqrt{13+2\sqrt{42}}=\sqrt{7}+2\sqrt{6}-\sqrt{5}`

Giải thích các bước giải:

`a)` `\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}`

`=\sqrt{{18-2\sqrt{17}}/2}-\sqrt{{18+2\sqrt{17}}/2}`

`=\sqrt{{17-2.\sqrt{17}.1+1^2}/2}-\sqrt{{17+2.\sqrt{17}.1+1^2}/2}`

`=\sqrt{{(\sqrt{17}-1)^2}/2}-\sqrt{{(\sqrt{17}+1)^2}/2}`

`=|{\sqrt{17}-1}/\sqrt{2}|-|{\sqrt{17}+1}/\sqrt{2}|`

`={\sqrt{17}-1}/\sqrt{2}-{\sqrt{17}+1}/\sqrt{2}`

`={\sqrt{17}-1-\sqrt{17}-1}/\sqrt{2}={-2}/\sqrt{2}=-\sqrt{2}`

Vậy: `\sqrt{9-\sqrt{17}}-\sqrt{9+\sqrt{17}}=-\sqrt{2}`

$\\$

`b)` `\sqrt{11-2\sqrt{30}}+\sqrt{13+2\sqrt{42}}`

`=\sqrt{6-2.\sqrt{6}.\sqrt{5}+5}+\sqrt{7+2.\sqrt{7}.\sqrt{6}+6}`

`=\sqrt{(\sqrt{6}-\sqrt{5})^2}+\sqrt{(\sqrt{7}+\sqrt{6})^2}`

`=|\sqrt{6}-\sqrt{5}|+|\sqrt{7}+\sqrt{6}|`

`=\sqrt{6}-\sqrt{5}+\sqrt{7}+\sqrt{6}`

`=\sqrt{7}+2\sqrt{6}-\sqrt{5}`

Vậy: `\sqrt{11-2\sqrt{30}}+\sqrt{13+2\sqrt{42}}=\sqrt{7}+2\sqrt{6}-\sqrt{5}`