Toán Lớp 8: So sánh cặp số sau : A= 2015. 2013 . ( 2014 ² + 1 ) và B = 2014^4
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Toán Lớp 8: So sánh cặp số sau : A= 2015. 2013 . ( 2014 ² + 1 ) và B = 2014^4
Comments ( 1 )
A = 2015.2013.\left( {{{2014}^2} + 1} \right)\\
= \left( {2014 + 1} \right)\left( {2014 – 1} \right).\left( {{{2014}^2} + 1} \right)\\
= \left( {{{2014}^2} – {1^2}} \right).\left( {{{2014}^2} + 1} \right)\\
= \left( {{{2014}^2} – 1} \right).\left( {{{2014}^2} + 1} \right)\\
= {\left( {{{2014}^2}} \right)^2} – {1^2}\\
= {2014^4} – 1\\
B = {2014^4}\\
{2014^4} – 1 < {2014^4} \Leftrightarrow A < B
\end{array}\)