`\sqrt((\sqrt(5)-3)^(2))-\sqrt(5*(-3)^(2))-4\sqrt(14-6\sqrt(5))` 20/07/2021 Bởi Isabelle `\sqrt((\sqrt(5)-3)^(2))-\sqrt(5*(-3)^(2))-4\sqrt(14-6\sqrt(5))`
Đáp án: `\sqrt{(\sqrt5-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt5}=-9` Giải thích các bước giải: `\sqrt{(\sqrt5-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt5}` `=|3-\sqrt5|-\sqrt{5.3^2}-4\sqrt{9-6\sqrt5+5}` `=3-\sqrt5-|3|\sqrt5-4\sqrt{3^2-2.3.\sqrt5+(\sqrt5)^2}` `=3-\sqrt5-3\sqrt5-4\sqrt{(3-\sqrt5)^2}` `=3-\sqrt5-3\sqrt5-4.|3-\sqrt5|` `=-4\sqrt5+3-4(3-\sqrt5)` `=-4\sqrt5+3-12+4\sqrt5` `=3-12` `=-9` Vậy `\sqrt{(\sqrt5-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt5}=-9` Bình luận
`\sqrt{(\sqrt{5}-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt{5}}` `=|\sqrt{5}-3|-3\sqrt{5}-4\sqrt{5-2.3.\sqrt{5}+9}` `=3-\sqrt{5}-3\sqrt{5}-4\sqrt{(\sqrt{5}-3)^2}` `=3-4\sqrt{5}-4|\sqrt{5}-3|` `=3-4\sqrt{5}-4(3-\sqrt{5})` `=3-4\sqrt{5}-12+4\sqrt{5}` `=-9` Bình luận
Đáp án:
`\sqrt{(\sqrt5-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt5}=-9`
Giải thích các bước giải:
`\sqrt{(\sqrt5-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt5}`
`=|3-\sqrt5|-\sqrt{5.3^2}-4\sqrt{9-6\sqrt5+5}`
`=3-\sqrt5-|3|\sqrt5-4\sqrt{3^2-2.3.\sqrt5+(\sqrt5)^2}`
`=3-\sqrt5-3\sqrt5-4\sqrt{(3-\sqrt5)^2}`
`=3-\sqrt5-3\sqrt5-4.|3-\sqrt5|`
`=-4\sqrt5+3-4(3-\sqrt5)`
`=-4\sqrt5+3-12+4\sqrt5`
`=3-12`
`=-9`
Vậy `\sqrt{(\sqrt5-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt5}=-9`
`\sqrt{(\sqrt{5}-3)^2}-\sqrt{5.(-3)^2}-4\sqrt{14-6\sqrt{5}}`
`=|\sqrt{5}-3|-3\sqrt{5}-4\sqrt{5-2.3.\sqrt{5}+9}`
`=3-\sqrt{5}-3\sqrt{5}-4\sqrt{(\sqrt{5}-3)^2}`
`=3-4\sqrt{5}-4|\sqrt{5}-3|`
`=3-4\sqrt{5}-4(3-\sqrt{5})`
`=3-4\sqrt{5}-12+4\sqrt{5}`
`=-9`