若x2+y2=10,xy=3,则(x-y)2=()

问题描述:

若x2+y2=10,xy=3,则(x-y)2=()

(x-y)2=2x+2y-2xy=10-2×3=4

(X-Y)2=X2-2XY+Y2=(X2+Y2)-2XY=10-2*3=4

(x-y)^2=x^2-2xy+y^2
=10-2*3
=10-6
=4

(x-2)^2=x^2+y^2-2xy=10-6=4

x+y=4,xy=3
(x+y)^2=16
x^2+2xy+y^2=16
x^2+y^2=16-6=10
x^2+y^2=10
x^2+y^2-2xy=10-2xy=10-6=4
(x-y)^2=4
x-y=2

(x-y)2
=x2+y2-2xy
=10-2*3
=4

答案是4
x2+y2=10
x2+y2-2xy=10-2xy
(x-y)2=4

(x-y)2=x2+y2-2xy=10-2×3=4

4