Question

(2x-y)^2-(x-y)(2x+3y)+(y-x)(x+y)

(2x-y)^2-(x-y)(2x+3y)+(y-x)(x+y) 求解啊，详细啊

Answer 1

解:设x=(X1,X2),y=(Y1,Y2).........[x,y是向量,(X1,X2),(Y1,Y2)都是坐标] 则a=y-x=(Y1-X1,Y2-X2),b=2x-y=(2X1-Y1,2X2-Y2) ∵|a|=|b|=1,即a＾2=b＾2=1 ∴a＾2=(Y1-X1,Y2-X2)＾2=1,即 Y1＾2+X1＾2-2X1Y1+Y2＾2+X2＾2-2X2Y2=1① b＾2=(2X1-Y1,2X2-Y2)＾2=1即4X1＾2+Y1＾2-4X1Y1+4X2＾2+Y2＾2-4X2Y2=1② 又∵a*b=0 即(Y1-X1,Y2-X2)*(2X1-Y1,2X2-Y2)=0 ∴化简得-2X1＾2-Y1＾2+3X1Y1-2X2＾2-Y2＾2+3X2Y2=0③ ①*3+③*2得:(Y1＾2+Y2＾2)-(X1＾2+X2＾2)=3④ ②*3+③*4得:4(X1＾2+X2＾2)-(Y1＾2+Y2＾2)=3⑤ 解方程组④⑤,得X1＾2+X2＾2=2 Y1＾2+Y2＾2=5 ∴|x|+|y|=二次根号项(X1＾2+X2＾2)+二次根号项(Y1＾2+Y2＾2) =根号2+根号5

Answer 2

(2x-y)^2-(x-y)(2x+3y)+(y-x)(x+y) =4x^2-4xy+y^2-(2x^2+xy-3y^2)+y^2-x^2 =4x^2-4xy+y^2-2x^2-xy+3y^2+y^2-x^2 =x^2-5xy+5y^2 =(x-5/2y)^2-5/4y^2 =(x-5/2y+√5/2y)(x-5/2y-√5/2y)