已知m-n=2+√3,n-p=2-√3,求m^2+n^2+q^2-mn-nq-mq的值

m-n=2+√3
n-p=2-√3
所以 两式相加 得：m-p=4
（m-n)^2=m^2-2mn+n^2=7+4√3
(n-p)^2=n^2-2np+p^2=7-4√3
(m-p)^2=m^2-2mp+p^2=16
三式相加:2(m^2+n^2+p^2-mn-np-mp)=7+7+16
既 m^2+n^2+p^2-mn-np-mp=15

是n-q=2-√3吧
m^2+n^2+q^2-mn-nq-mq
=[(m^2-2mn+n^2)+(n^2-2nq+q^2)+(q^2-2mq+m^2)]/2
=[(m-n)^2+(n-q)^2+(q-m)^2]/2
=[(2+√3)^2+(2-√3)^2+(-4)^2]/2
=33/2

m^2+n^2+q^2-mn-nq-mq
=2*(m^2+n^2+q^2-mn-nq-mq)/2
=(m^2+n^2+q^2+m^2+n^2+q^2-2mn-2nq-2mq)/2
=(m^2+n^2-2mn+q^2+m^2-2mq+n^2+q^2-2nq)/2
=[(m-n)^2*(m-q)^2*(n-q)^2]/2
已知m-n=2+√3,n-p=2-√3,
所以m-q=m-n+n-p=2+√3+2-√3=4
代入化简计算得
m^2+n^2+q^2-mn-nq-mq=15

m-n=2+1.732①
n-p=2-1.732②
则m-p=4
m^2+n^2+p^2-mn-np-mp=1/2[(m-p)^2+(m-n)^2+(n-p)^2]
=15

p和q应该打错了

(m-n)+(n-p)=m-p=4
（m-p）^2+(n-p)^2+(m-n)^2
=2(m^2+n^2+p^2-mn-np-mp)
=4^2+(2+√3)^2+(2-√3)^2
=30
所以m^2+n^2+p^2-mn-np-mp=15

没法做，m^2+n^2+q^2-mn-nq-mq中的q在前面没有。