<t>Here is one simple, but less tight lower bound:(a^2 + b^2 + c^2 )^2 - (1/M)(ab(a^2-b^2)...) = a^4 + b^4 + 2a^2b^2 - (1/M)ab^3 +(1/M)a^3b ... fill in similar terms containing b, c and c,aNote that:a^4 + b^4 + c^4 + 2a^2b^2 - Mab^3 +Ma^3b is of the form (a^2 + b^2 + k * a * b)^2, if we can find the...