Question

2009全国初中数学竞赛决赛解答题

Answer 1

1.(1)x^2=(2t-1)x-c

x^2-(2t-1)x+c=0

△=4t^2-4t+1-4c≥0

根据韦达定理x1x2=c,x1+x2=2t-1

(x1)^2+(x2)^2

=(x1+x2)^2-2x1x2

=4t^2-4t+1-2c=t^2+2t-3

得3t^2-6t+4=2c

△=-2t^2+8t-7≥0

解得(4-根号2)/2≤t≤(4+根号2)/2

(2)3t^2-6t+4=2c

c=3(t-1)^2+1

因为(4-根号2)/2≤t

所以当t=(4-根号2)/2时,cmin=(11-6*根号2)/2

2.有.x=1,y=3时.