If $abcd=1$,where $a,b,c,d$ are positive reals,then find the minimum value of $a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd$. If $abcd=1$,where $a,b,c,d$ are positive reals,then find the minimum value of $a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd$.

Let $E=a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd=(a+b+c+d)^2-(ab+ac+ad+bc+bd+cd)$
I do not know how to use $abcd=1$ in this question to get the minimum value of the expression. 

with AM-GM, we get
a²+b²+c²+d² ≥ 4√((abcd)²) = 4
ab+ac+ad+bc+bd+cd ≥ 6√((abcd)³) = 6
minimum value of a²+b²+c²+d²+ab+ac+ad+bc+bd+cd is 4+6 = 10 when a=b=c=d=1.
