`Rút gọn: ` $\sqrt[]{17-12\sqrt[]{2}}$ `-` $\sqrt[]{9+4\sqrt[]{2}}$ 22/09/2021 Bởi Aaliyah `Rút gọn: ` $\sqrt[]{17-12\sqrt[]{2}}$ `-` $\sqrt[]{9+4\sqrt[]{2}}$
Đáp án: `= 2 – 4\sqrt2` Giải thích các bước giải: `\sqrt(17-12\sqrt2) – \sqrt(9+4\sqrt2)` `= \sqrt(9+8-12\sqrt2) – \sqrt(1+8+4\sqrt2)` `= \sqrt(3^2-2.3.2\sqrt2+(2\sqrt2)^2) – \sqrt(1^2 + 2.1.2\sqrt2 + (2\sqrt2)^2)` `= \sqrt((3-2\sqrt2)^2) – \sqrt((1+2\sqrt2)^2)` `= 3 – 2\sqrt2 – (1 + 2\sqrt2)` `= 3 – 2\sqrt2 – 1 – 2\sqrt2` `= 2 – 4\sqrt2` Bình luận
$\sqrt[]{17-12\sqrt[]{2}} – \sqrt[]{9+4\sqrt[]{2}}$ $ = \sqrt[]{(3-2\sqrt[]{2})^2} – \sqrt[]{(2\sqrt[]{2}+1)^2}$ $ = 2-4\sqrt[]{2}$ Bình luận
Đáp án: `= 2 – 4\sqrt2`
Giải thích các bước giải:
`\sqrt(17-12\sqrt2) – \sqrt(9+4\sqrt2)`
`= \sqrt(9+8-12\sqrt2) – \sqrt(1+8+4\sqrt2)`
`= \sqrt(3^2-2.3.2\sqrt2+(2\sqrt2)^2) – \sqrt(1^2 + 2.1.2\sqrt2 + (2\sqrt2)^2)`
`= \sqrt((3-2\sqrt2)^2) – \sqrt((1+2\sqrt2)^2)`
`= 3 – 2\sqrt2 – (1 + 2\sqrt2)`
`= 3 – 2\sqrt2 – 1 – 2\sqrt2`
`= 2 – 4\sqrt2`
$\sqrt[]{17-12\sqrt[]{2}} – \sqrt[]{9+4\sqrt[]{2}}$
$ = \sqrt[]{(3-2\sqrt[]{2})^2} – \sqrt[]{(2\sqrt[]{2}+1)^2}$
$ = 2-4\sqrt[]{2}$