Chứng minh rằng: `sqrt(17 – 12sqrt(2))` `+2sqrt(2)` `=3` Em cảm ơn trước ạ!

$\sqrt{17-12\sqrt2}+2\sqrt2$

$=\sqrt{17-2.3.2\sqrt2}+2\sqrt2$

$=\sqrt{3^2-2.3.(2\sqrt2)+(2\sqrt2)^2}+2\sqrt2$

$=\sqrt{(3-2\sqrt2)^2}+2\sqrt2$

$=|3-2\sqrt2|+2\sqrt2$

$=3-2\sqrt2+2\sqrt2$ (do $9>8\to \sqrt9>\sqrt8\to 3>2\sqrt2$)

$=3$