Đáp án:
a) A>B
b) A<B
c) \(\left[ \begin{array}{l}x=-4\\x=-5\\x=-6\end{array} \right.\)
Giải chi tiết
a) Có: \(A=33\\=3.11\\=3\sqrt[3]{1331}>3\sqrt[3]{133}\\\to A>B\)
b) Có: \(A=5\sqrt[3]{6}\\=\sqrt[3]{125}.\sqrt[3]{6}\\=\sqrt[3]{125.6}\\=\sqrt[3]{750} \, \, \, (1)\\B=6\sqrt[3]{5}\\=\sqrt[3]{216}.\sqrt[3]{5}\\=\sqrt[3]{5.216}\\=\sqrt[3]{1080} \, \, \, (2)\)
Do (1)<(2) \(\to\) \(A<B\)
c) \(\sqrt[3]{5+x}-x=5\\\Rightarrow\sqrt[3]{5+x}=5+x\\\Rightarrow(\sqrt[3]{5+x})^3=(5+x)^3\\\Rightarrow5+x=5^3+3.5^2x+3.5x^2+x^3\\\Rightarrow125+75x+15x^2+x^3-5-x=0\\\Rightarrow x^3+15x^2+74x+120=0\\\Rightarrow(x^3+6x^2)+(9x^2+54x)+(20x+120)=0\\\Rightarrow x^2(x+6)+9x(x+6)+20(x+6)=0\\\Rightarrow (x^2+9x+20)(x+6)=20\\\Rightarrow [(x^2+4x)+(5x+20)](x+6)=0\\\Rightarrow (x+5)(x+4)(x+6)=0\\\Rightarrow \left[ \begin{array}{l}x=-4\\x=-5\\x=-6\end{array} \right.\)
