Question

So sánh P và Q biết ;

P = \(\dfrac{2013.2014-1007.4030}{2014^2-2011.2014}\)

Q = -\(\dfrac{214263}{142842}\)

Answer 1

\(P=\dfrac{2013.2014-1007.4030}{2014^2-2011.2014}\)

\(P=\dfrac{2013.2014-1007.2.2015}{2014^2-2011.2014}\)

\(P=\dfrac{2013.2014-2014.2015}{2014^2-2011.2014}\)

\(P=\dfrac{2014.\left(2013-2015\right)}{2014.\left(2014-2011\right)}\)

\(P=-\dfrac{2}{3}\)

\(Q=-\dfrac{214263}{142862}=-\dfrac{214263:71421}{142862:71421}=-\dfrac{3}{2}\)

Vì \(-\dfrac{2}{3}>-\dfrac{3}{2}\)nên P>Q

Answer 2

\(P=\dfrac{2013.2014-1007.4030}{2014^2-2011.2014}\)

\(P=\dfrac{2013.2014-1007.4030}{2014.2014-2011.2014}\)

\(P=\dfrac{2013.2.1007-1007.4030}{2014\left(2014-2011\right)}\)

\(P=\dfrac{4026.1007-1007.4030}{2014.3}\)

\(=\dfrac{1007.\left(4026-4030\right)}{1007.2.3}\)

\(=\dfrac{1007.-4}{1007.6}=\dfrac{-4}{6}=\dfrac{-2}{3}\)

\(Q=\dfrac{214263}{142842}=-\dfrac{3}{2}\)

\(-\dfrac{3}{2}< -\dfrac{2}{3}\Rightarrow P>Q\)