Question

（7）若x(y-1)-y(x-1)=4,求x²+y²/2-xy的值

Answer 1

x(y-1)-y(x-1)=4

xy-x-xy+y=4

-x+y=4

∴x-y=-4

(x²+y²)/2-xy=(x²-2xy+y²)/2=(x-y)²/2=8

a=1/20 x+20,b=1/20 x+19,c=1/20 x+21

∴a-b=1

b-c=-2

c-a=1

a²+b²+c²-ab-bc-ac

=1/2[(a-b)²+(b-c)²+(c-a)²]

=1/2[1²+(-2)²+1²]

=3