设a，b，c是正实数，满足b+c≥a，则bc+ca+b的最小值为．

Question

设a，b，c是正实数，满足b+c≥a，则 (b)/(c)+ (c)/(a+b)的最小值为___．

Answer 1

∵a，b，c是正实数，满足b+c≥a
∴(b)/(c)+(c)/(a+b)
≥(b)/(c)+(c)/(2b+c)
=(b)/(c)+(1)/((2b)/(c)+1)
=(1)/(2)（(2b)/(c)+1)+(1)/((2b)/(c)+1)-(1)/(2)
≥√(2)-(1)/(2)（当且仅当b+c=a且(b)/(c)=(√(2)-1)/(2)时取等号）
故答案为：√(2)-(1)/(2)．