问题在条件a,b,c∈R+且a+b+c=1下,是不是a2+b2+c2+λabc(λ∈R)一定有最值?文[1]探讨了此问题,并得出结果:当λ≤2时,a2+b2+c2+λabc有最小值λ+9/27,且在a=b=c=1/3时取得;当λ≥18时,a2+b2+c2+λabc有最大值λ+9/27,且在a=b=c=1/3时取得; The question is whether a2 + b2 + c2 + λabc (λ∈R) must have the most value under the conditions a, b, c∈R + and a + b + c = 1 This problem is discussed in [1] The result: When λ≤2, a2 ​​+ b2 + c2 + λabc has the minimum value λ + 9/27 and is obtained when a = b = c = 1/3; when λ≥18, a2 + b2 + c2 + λabc has a maximum of λ + 9/27 and is obtained when a = b = c = 1/3;