X-Y=1,X^3-Y^3=2问X^4-Y^4的值
问题描述：
X-Y=1,X^3-Y^3=2问X^4-Y^4的值
答
X^3-Y^3 =(X-Y)(X^2+XY+Y^2) =X^2+XY+Y^2 //因为X-Y=1 =(X-Y)^2+3XY =1+3XY=2 所以XY=1/3.(X+Y)^2 =X^2+2XY+Y^2 =X^2-2XY+Y^2+4XY =(X-Y)^2+4XY =1+4/3 = 7/3 所以X+Y=+/-sqrt(7/3).X^4-Y^4 =(X^2+Y^2)(X^2-Y^2) =((X-Y)^2+2XY)(X+Y)(X-Y) =(1+2/3)(+/-sqrt(7/3)) =+/-(5/3)*sqrt(7/3)