Question

so sánh:

1)A= \(2013.2015+2014.2016\) và B= \(2014^2+2015^2-2\)

 

Answer 1

Dễ c/m đẳng thức: \(\left(n-1\right)\left(n+1\right)=n^2-1\)

Lúc đó: \(A=2014^2-1+2015^2-1=2014^2+2015^2-2=B\)

Vậy A = B

Answer 2

\(A=2013.2015+2014.2016\)

   \(=\left(2015-2\right).2015+2014\left(2014+2\right)\)

   \(=(2015^2-4030)+(2014^2+4028)\)

   \(=\left(2015^2+2014^2\right)-\left(4030-4028\right)\)

  \(=2014^2+2015^2-2\)

\(\Rightarrow A=B\)