Prove that, for all real numbers a,b and c,

(a+b+c)^2 <= 3(a^2 + b^2 + c^2)

Further, show that 3 is the smallest real number with this property.

I haven't been able to prove it yet - all i've done is go around in circles and play with signs. The second part of the question has me really confused. If it applies for all real numbers, how can i prove that 3 is the smallest real number with this property?