đặt \(\sqrt{2013}=x;\sqrt{2014}=y\)
=>A=\(\left(x+y\right)^4-2.\left(2013+2014\right)\left(x+y\right)^2+2015\)
=>A=\(\left(x+y\right)^4-2.\left(x^2+y^2\right)\left(x+y\right)^2+\left(x^2+y^2\right)^2-\left(x^2+y^2\right)^2\)
=>A=\(\left(x^2+2xy+y^2-x^2-y^2\right)-x^4-2x^2y^2-y^4+2015\)
=>A=\(4x^2y^2-x^4-2x^2y^2-y^4+2015=2015-\left(x^2-y^2\right)^2=2015-\left(2013-2014\right)^2=2014\)
Đặt căn 2013=x ; căn 2014 =y
=> 2(x2+y2)=8054; y2-x2=1
thay vào đc pt: (x+y)4-2(x2+y2)(x+y)2+2015
=(x+y)2(x2+2xy+y2-2x2-2y2)+2015
=-(x+y)2(x-y)2+2015
=-(x2-y2)2+2015
=-1+2015 (vì y2-x2=1)
=2014
