Đáp án + 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)/2}-\sqrt{(17+2\sqrt{17}+1)/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{17}+1))/\sqrt{2}`
`=(-2)/\sqrt{2}`
`=-\sqrt{2}`
Hoặc đề là `\sqrt{9-\sqrt{17}}\sqrt{9+\sqrt{17}}`
`=\sqrt{(9-\sqrt{17})(9+\sqrt{17})}`
`=\sqrt{81-17}`
`=\sqrt{64}`
`=8`
b) `(\sqrt{6}+\sqrt{14})/(2\sqrt{3} +\sqrt{28})`
`=(\sqrt{2}(\sqrt{3}+\sqrt{7}))/(\sqrt{4}(\sqrt{3}+\sqrt{7}))`
`=\sqrt{2}/\sqrt{4}`
`=1/\sqrt{2}`
`=\sqrt{2}/2`
