Giải thích các bước giải:
Ta có :
$5x^2+5y^2+8xy-2x+3y+2=0$
$\to 5x^2+2x(4y-1)+5y^2+3y+2=0$
$\to 25x^2+10x(4y-1)+25y^2+15y+10=0$
$\to 25x^2+10x(4y-1)+(4y-1)^2+9y^2+6y+1=0$
$\to (5x+4y-1)^2+(3y+1)^2=0$
$\to y=\dfrac{-1}{3}, x=\dfrac{7}{15}$
$\to M=(\dfrac{-6}{5})^{2013}+(\dfrac{-31}{15})^2+2.1^{2015}+2015$