Chứng minh rằng: `sqrt(17 – 12sqrt(2))` `+2sqrt(2)` `=3` Em cảm ơn trước ạ! 06/07/2021 Bởi Lyla 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 $9>8\to \sqrt9>\sqrt8\to 3>2\sqrt2$) $=3$ Bình luận
Đáp án: `sqrt{17-12sqrt2}+2sqrt2` `=sqrt{9-2.3.2sqrt2+8}+2sqrt2` `=sqrt{(3-2sqrt2)^2}+2sqrt2` `=|3-2sqrt2|+2sqrt2` `=3-2sqrt2+2sqrt2(do \ 3>2sqrt2)` `=3`. Bình luận
$\sqrt{17-12\sqrt2}+2\sqrt2$
$=\sqrt{17-2.3.2\sqrt2}+2\sqrt2$
$=\sqrt{3^2-2.3.(2\sqrt2)+(2\sqrt2)^2}+2\sqrt2$
$=\sqrt{(3-2\sqrt2)^2}+2\sqrt2$
$=|3-2\sqrt2|+2\sqrt2$
$=3-2\sqrt2+2\sqrt2$ (do $9>8\to \sqrt9>\sqrt8\to 3>2\sqrt2$)
$=3$
Đáp án:
`sqrt{17-12sqrt2}+2sqrt2`
`=sqrt{9-2.3.2sqrt2+8}+2sqrt2`
`=sqrt{(3-2sqrt2)^2}+2sqrt2`
`=|3-2sqrt2|+2sqrt2`
`=3-2sqrt2+2sqrt2(do \ 3>2sqrt2)`
`=3`.