Question

已知x,y为实数,且满足y=√(x-1/2)+√(1/2-x)+1/2,求4x+|2y-1|-√(y^-2y+1)的值.

急用.

Answer 1

因为x-1/2大于或等于0
1/2-x也大于或等于0，所以x=1/2，y=1/2
所以原式=4*1/2+|2*1/2-1|-√[1/2^(-2*1/2+1)]
=2+0-1
=2-1
=1

Answer 2

因为√(x-1/2)+√(1/2-x)有意义
所以(x-1/2)>=0 (1/2-x)>=0
则x-1/2=1/2-x=0
x=1/2 代入式子
则y=1/2
则原式=4*1/2+|2*1/2-1|-√[1/2^(-2*1/2+1)]
=2+0-√(1/2^0)
=2-1
=1