Question

已知a=200x+2007,b=200x+2008,c=200x+2009,求多项式a^2+b^2+c^2-ab-b

Answer 1

[1] x^2+y^2=(x+y)^2-2xy=28

[2] x^4+y^4=(x^2+y^2)^2-2(x^2)(y^2)=784-32=752

3.xy=[(x+y)^2-(x-y)^2]/4=-4

4.证明：因为x+y=1

所以y=1-x

所以x^3+y^3-xy

=x^3+(1-x)^3-x(1-x)

=4x^2-4x+1

=(2x-1)^2>=0

syx^3+y^3-xy的值是非负数