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![](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)
cho x = \(\sqrt[3]{38+17\sqrt{5}}+\sqrt[3]{38-17\sqrt{5}}\)
Tính C= \(\left(x^3+3x+1935\right)2018\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x=\sqrt[3]{38+17\sqrt{5}}+\sqrt[3]{38-17\sqrt{5}}=\sqrt[3]{5\sqrt{5}+3.5.2+3.\sqrt{5}.4+8}+\sqrt[3]{8-3.4.\sqrt{5}+3.2.5-5\sqrt{5}}=\sqrt[3]{\left(2+\sqrt{5}\right)^3}+\sqrt[3]{\left(2-\sqrt{5}\right)^3}=2+\sqrt{5}+2-\sqrt{5}=4\)Vậy C=(43+3.4+1935)2018=2011.2018=4058198
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3=76+3\sqrt[3]{\left(38-17\sqrt{5}\right)\left(38+17\sqrt{5}\right)}\left(\sqrt[3]{38-17\sqrt{5}}+\sqrt[3]{38+17\sqrt{5}}\right)\)
\(\Leftrightarrow x^3=76-3x\)
\(\Leftrightarrow x^3+3x-76=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^2+4x+19\right)=0\)
\(\Leftrightarrow x=4\)
\(\Rightarrow x^3-3x^2-2x-8=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}{\sqrt{5}+3-\sqrt{5}}=\dfrac{3}{3}=1\)
\(A=\left(3\cdot1+8\cdot1+2\right)^{2018}=13^{2018}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt[3]{17\sqrt{5}-38}\text{=}\sqrt[3]{5\sqrt{5}-30+12\sqrt{5}-8}\)
\(\text{=}\sqrt[3]{\left(\sqrt{5}-2\right)^3}\)
\(\text{=}\sqrt{5}-2\)
\(x=\sqrt[3]{17\sqrt{5}+38}-\sqrt[3]{17\sqrt{5}-38}\)
\(=\sqrt[3]{\left(\sqrt{5}+2\right)^3}+\sqrt[3]{\left(\sqrt{5}-2\right)^3}\)
\(=\sqrt{5}+2+\sqrt{5}-2\)
\(=2\sqrt{5}\)
Dùng cách phổ thông hơn bạn nhé!
\(x^3=17\sqrt{5}+38-17\sqrt{5}+38-3\sqrt[3]{\left(17\sqrt{5}+38\right)\left(17\sqrt{5}-38\right)}x\)
\(=76-3x\sqrt[3]{1445-1444}\)
\(=76-3x\)
\(\Rightarrow x^3+3x-76=0\)
\(\Leftrightarrow x^3-16x+19x-76=0\)
\(\Leftrightarrow x\left(x-4\right)\left(x+4\right)+19\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^2+4x+19\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left[\left(x+2\right)^2+15\right]=0\)
Vì [...] > 0
Nên x - 4 = 0
=> x = 4