求证1/a+1/b+1/c≥1/√ab+1/√bc+1/√acabc都大于0,√是根号

求证1/a+1/b+1/c≥1/√ab+1/√bc+1/√acabc都大于0,√是根号
求证1/a+1/b+1/c≥1/√ab+1/√bc+1/√ac
abc都大于0,√是根号

求证1/a+1/b+1/c≥1/√ab+1/√bc+1/√acabc都大于0,√是根号
∵abc都大于0,
∴(1/√a)²+(1/√b)²≥2/(√ab)
1/a+1/b≥2/(√ab)……①
同理可得：
1/b+1/c≥2/(√bc)……②
1/c+1/a≥2/(√ca)……③
①+②+③得：
1/a+1/b1+1/c≥1/(√ab)+1/(√bc)+1/(√ca)