Question

Giải giúp

Answer 1

\(A=\sqrt[3]{49.7}+\sqrt[3]{4.7}-\sqrt[3]{14.7}+\sqrt[3]{2.49}+\sqrt[3]{2.4}-\sqrt[3]{14.2}\)

\(=7+\sqrt[3]{28}-\sqrt[3]{98}+\sqrt[3]{98}+2-\sqrt[3]{28}\)

\(=9\)

\(B=\sqrt[3]{46\sqrt{5}-61}-\sqrt[3]{46\sqrt[]{5}+61}\)

\(=\sqrt[3]{40\sqrt[]{5}-60+6\sqrt[]{5}-1}-\sqrt[]{40\sqrt[]{5}+60+6\sqrt[]{5}+1}\)

\(=\sqrt[3]{\left(2\sqrt[]{5}\right)^3-3.\left(2\sqrt[]{5}\right)^2+3.2\sqrt[]{5}.1-1^3}-\sqrt[3]{\left(2\sqrt[]{5}\right)^3+3.\left(2\sqrt[]{5}\right)^2+32\sqrt[]{5}+1}\)

\(=\sqrt[3]{\left(2\sqrt[]{5}-1\right)^3}-\sqrt[3]{\left(2\sqrt[]{5}+1\right)^3}\)

\(=2\sqrt[]{5}-1-2\sqrt[]{5}-1\)

\(=-2\)

Answer 2

\(C=\sqrt[3]{2+\sqrt[]{5}}+\sqrt[3]{2-\sqrt[]{5}}\)

\(\Rightarrow C^3=4+3\left(\sqrt[3]{2+\sqrt[]{5}}+\sqrt[3]{2-\sqrt[]{5}}\right)\sqrt[3]{\left(2+\sqrt[]{5}\right)\left(2-\sqrt[]{5}\right)}\)

\(\Rightarrow C^3=4-3C\)

\(\Rightarrow C^3+3C-4=0\)

\(\Leftrightarrow\left(C-1\right)\left(C^2+C+4\right)=0\)

\(\Leftrightarrow C=1\)

\(D=\dfrac{\sqrt[3]{4}-\sqrt[3]{2}+1}{\left(\sqrt[3]{2}+1\right)\left(\sqrt[3]{4}-\sqrt[3]{2}+1\right)}-\dfrac{\sqrt[3]{4}-\sqrt[3]{2}}{3}\)

\(=\dfrac{\sqrt[3]{4}-\sqrt[3]{2}+1}{\left(\sqrt[3]{2}\right)^3+1^3}-\dfrac{\sqrt[3]{4}-\sqrt[3]{2}}{3}=\dfrac{\sqrt[3]{4}-\sqrt[3]{2}+1}{3}-\dfrac{\sqrt[3]{4}-\sqrt[3]{2}}{3}\)

\(=\dfrac{1}{3}\)