CHÚC BẠN HỌC TỐT !!!!!!!!!!
Đáp án:
Giải thích các bước giải:
$a)$
$VT = \sqrt{2 + \sqrt{3}} + \sqrt{2 - \sqrt{3}}$
$= \dfrac{1}{\sqrt{2}}.\sqrt{2}.(\sqrt{2 + \sqrt{3}} + \sqrt{2 - \sqrt{3}})$
$= \dfrac{1}{\sqrt{2}}.(\sqrt{4 + 2\sqrt{3}} + \sqrt{4 - 2\sqrt{3}})$
$= \dfrac{1}{\sqrt{2}}.(\sqrt{3 + 2\sqrt{3} + 1} + \sqrt{3 - 2\sqrt{3} + 1})$
$= \dfrac{1}{\sqrt{2}}.[\sqrt{(\sqrt{3} + 1)^2} + \sqrt{(\sqrt{3} - 1)^2}]$
$= \dfrac{1}{\sqrt{2}}.(|\sqrt{3} + 1| + |\sqrt{3} - 1|)$
$= \dfrac{1}{\sqrt{2}}.(\sqrt{3} + 1 + \sqrt{3} - 1)$
$= \dfrac{1}{\sqrt{2}}.2\sqrt{3}$
$= \sqrt{6} = VP$ $(đpcm)$
$b)$
$VT =$ `\sqrt{4/{(2 - \sqrt{5})^2}} - \sqrt{4/{(2 + \sqrt{5})^2}}`
`= 2/{|2 - \sqrt{5}|} - 2/{|2 + \sqrt{5}|}`
`= 2/{\sqrt{5} - 2} - 2/{\sqrt{5} + 2}`
`= {2.(\sqrt{5} + 2) - 2.(\sqrt{5} - 2)}/{(\sqrt{5} - 2).(\sqrt{5} + 2)`
`= {2\sqrt{5} + 4 - 2\sqrt{5} + 4}/{5 - 4}`
`= 8` $= VP$ $(đpcm)$
