VP là ` \sqrt(6)`
Áp dụng bất đẳng thức Cauchy dạng ` \sqrt(ab) \le (a+b)/2`
` \sqrt (2/3 (a+b)) \le ( 2/3 + a +b)/2`
` \sqrt( 2/3 (a+c) \le ( 2/3 + a +c)/2`
` \sqrt( 2/3 (b+c) ) \le ( 2/3 + b + c)/2`
` \to \sqrt (2/3 (a+b))+ \sqrt( 2/3 (a+c)) + \sqrt( 2/3 (b+c)) \le ( 2(a+b+c) + 2)/2 = 2`
`\to \sqrt(2/3) . (\sqrt(a+b) + \sqrt(a+c) + \sqrt(b+c)) \le 2`
`\to (\sqrt(a+b) + \sqrt(a+c) + \sqrt(b+c)) \le \sqrt(6)` (đpcm)
Dấu `=` xảy ra khi ` a= b = c = 1/3`
