Question

So sánh: \(C=\sqrt[3]{2011}-\sqrt[3]{2010.}\) và \(B=\sqrt[3]{2010}-\sqrt[3]{2009}\)

Answer 1

\(C=\sqrt[3]{2011}-\sqrt[3]{2010}=\frac{2011-2010}{\left(\sqrt[3]{2011^2}+\sqrt[3]{2011}\sqrt[3]{2010}+\sqrt[3]{2010^2}\right)}=\frac{1}{\left(\sqrt[3]{2011^2}+\sqrt[3]{2011}\sqrt[3]{2010}+\sqrt[3]{2010^2}\right)}\)

\(B=\sqrt[3]{2010}-\sqrt[3]{2009}=\frac{2010-2009}{\left(\sqrt[3]{2010^2}+\sqrt[3]{2010}\sqrt[3]{2009}+\sqrt[3]{2009^2}\right)}=\frac{1}{\left(\sqrt[3]{2010^2}+\sqrt[3]{2010}\sqrt[3]{2009}+\sqrt[3]{2009^2}\right)}\)Vì \(\left(\sqrt[3]{2011^2}+\sqrt[3]{2011}\sqrt[3]{2010}+\sqrt[3]{2010^2}\right)>\left(\sqrt[3]{2010^2}+\sqrt[3]{2010}\sqrt[3]{2009}+\sqrt[3]{2009^2}\right)\)

\(B< C\)

Answer 2

lập phương B , C lên 

Answer 3

Không tính giá trị đâu mấy cậu. Tuôi vừa nghĩ ra, lấy \(C-B=\sqrt[3]{2011}-\sqrt[3]{2009}>0.\)Dẫn tới  C>B.