当y-x=5时,求x^2-y^2+5x+5y+2006的值

当y-x=5时,求x^2-y^2+5x+5y+2006的值
当y-x=5时,求x^2-y^2+5x+5y+2006的值

当y-x=5时,求x^2-y^2+5x+5y+2006的值
2006
x^2-y^2+5x+5y+2006
=(x+y)(x-y)+5(x+y)+2006
=(x+y)(x-y+5)+2006
=(x+y)(-5+5)+2006
=2006

x²-y²+5x+5y+2006
=(x+y)(x-y)+5(x+y)+2006
=(x+y)(x-y+5)+2006
=(x+y)[-(y-x)+5]+2006
=(x+y)(-5+5)+2006
=2006

由已知:原式=(X+Y)*(X-Y)+5*(X+Y)+2006=(X-Y+5)*(X+Y)=2006,
又因为:Y-X=5,即X-Y+5=0,
代入可得:原式=0*(X+Y)+2006=2006.
答案是2006