设abc均为不小于3的实数,则(根号a-2)+(根号b+1)+[1-(根号c-1)]的绝对值的最小值是______

题目

设abc均为不小于3的实数,则(根号a-2)+(根号b+1)+[1-(根号c-1)]的绝对值的最小值是______

答案

∵a≥3,b≥3,c≥3
∴a-2≥1,b+1≥4,c-1≥2
√(a-2)+√(b+1)+|1-√(c-1)|
=√(a-2)+√(b+1)+√(c-1)-1
≥1+2+√2-1
=2+√2