Rút gọn các biểu thức:
a) A= \(\frac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}\sqrt[3]{4}\)
b) B= \(\left(\frac{1}{2}\sqrt[3]{2}-\frac{1}{4}\sqrt[3]{16}\right).\sqrt[3]{4}\)
c) C= \(\sqrt[3]{\left(\sqrt{2}+1\right)\left(3+2\sqrt{2}\right)}\)
d) D= \(\sqrt[3]{3+3\sqrt[3]{2}+3\sqrt[3]{4}}\)
e) E= \(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}\)
Ok, ko chép đề nha =))
\(A=\sqrt[3]{\frac{135}{5}}-\sqrt[3]{54\cdot4}\\ =\sqrt[3]{27}-\sqrt[3]{216}=3-6=-3\)
\(B=\frac{1}{2}\cdot\sqrt[3]{2\cdot4}-\frac{1}{4}\cdot\sqrt[3]{16\cdot4}\\ =\frac{1}{2}\cdot\sqrt[3]{8}-\frac{1}{4}\cdot\sqrt[3]{64}\\ =\frac{1}{2}\cdot2-\frac{1}{4}\cdot4=1-1=0\)
\(C=\sqrt[3]{\left(\sqrt{2}+1\right)\left(3+2\sqrt{2}\right)}\\ =\sqrt[3]{\left(\sqrt{2}+1\right)\left(2+2\cdot\sqrt{2}\cdot1+1\right)}\\ =\sqrt[3]{\left(\sqrt{2}+1\right)\left(\sqrt{2}+1\right)^2}\\ =\sqrt[3]{\left(\sqrt{2}+1\right)^3}=\sqrt{2}+1\)
\(D=\sqrt[3]{\frac{3\left(\sqrt[3]{2}-1\right)\left(1+\sqrt[3]{2}+\sqrt[3]{4}\right)}{\sqrt[3]{2}-1}}\\ =\sqrt[3]{\frac{3\left(2-1\right)}{\sqrt[3]{2}-1}}\\ =\sqrt[3]{\frac{3}{\sqrt[3]{2}-1}}\) (chịu, ko bít rút thêm :V)
\(E=\) chịu nốt =))
Chúc bạn học tốt nha
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