tính A= \(\sqrt[3]{3-\sqrt{17}}+\sqrt[3]{3-\sqrt{17}}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(a^3=\left(\sqrt[3]{3+\sqrt{17}}+\sqrt[3]{3-\sqrt{17}}\right)^3\)
\(=3+\sqrt{17}+3-\sqrt{17}+3\sqrt[3]{\left(3+\sqrt{17}\right)\left(3-\sqrt{17}\right)}\left(\sqrt[3]{3+\sqrt{17}}+\sqrt[3]{3-\sqrt{17}}\right)\)
(\(\left(a+b\right)^3=a^3+b^3+3ab\left(a+b\right)\) )
\(=6+3\sqrt[3]{-8}.a=6-6a\)
\(\Rightarrow a^3+6a-6=0\Rightarrow a^3+6a-5=1\)
\(\Rightarrow A=1^{2019}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
\(=\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
\(=\sqrt{9+2.3.\sqrt{8}+8}+\sqrt{9-2.3.\sqrt{8}+8}\)
\(=\sqrt{\left(3+\sqrt{8}\right)^2}+\sqrt{\left(3-\sqrt{8}\right)^2}=\left|3+\sqrt{8}\right|+\left|3-\sqrt{8}\right|\)
\(=3+\sqrt{8}+3-\sqrt{8}\) (do \(3>\sqrt{8}\))
\(=6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
đây là toán lớp 9 mà
trả lời chỉ để lấy tích thời mọi người tích giùm hihi
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a^3=38+17\sqrt{5}+38-17\sqrt{5}+3\cdot a\cdot\sqrt[3]{\left(38\right)^2-\left(17\sqrt{5}\right)^2}\)
=>a^3=76-3a
=>a^3+3a-76=0
=>a=4
f(x)=(4^3+3*4+1940)^2016=2016^2016
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3=3+2\sqrt{2}+3-2\sqrt{2}+3\cdot\sqrt[3]{\left(3+2\sqrt{2}\right)\left(3-2\sqrt{2}\right)}\left(\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\right)\\ \Leftrightarrow x^3=6+3x\sqrt[3]{1}\\ \Leftrightarrow x^3-3x=6\)
\(y^3=17+12\sqrt{2}+17-12\sqrt{2}+3\sqrt[3]{\left(17-12\sqrt{2}\right)\left(17+12\sqrt{2}\right)}\left(\sqrt[3]{17-12\sqrt{2}}+\sqrt[3]{17+12\sqrt{2}}\right)\\ \Leftrightarrow y^3=34+3x\sqrt[3]{1}\\ \Leftrightarrow y^3-3y=34\)
Thay vào P, ta được
\(P=x^3+y^3-3x-3y+1979\\ P=\left(x^3-3x\right)+\left(y^3-3y\right)+1979\\ P=6+34+1979=2019\)
\(x^3=6+3\sqrt[3]{\left(3+2\sqrt[]{2}\right)\left(3-2\sqrt[]{2}\right)}\left(\sqrt[3]{3+2\sqrt[]{2}}+\sqrt[3]{3-2\sqrt[]{2}}\right)\)
\(\Rightarrow x^3=6+3x\)
\(\Rightarrow x^3-3x=6\)
Tương tự:
\(y^3=34+3\sqrt[3]{\left(17+12\sqrt[]{2}\right)\left(17-12\sqrt[]{2}\right)}\left(\sqrt[3]{17+12\sqrt[]{2}}+\sqrt[3]{17-12\sqrt[]{2}}\right)\)
\(\Rightarrow y^3=34+3y\)
\(\Rightarrow y^3-3y=34\)
Do đó:
\(P=\left(x^3-3x\right)+\left(y^3-3y\right)+1979=6+34+1979=...\)
Đề sai à bạn
mk ghi nhầm =))