若n的平方+3n=1,求n(n+1)(n+2)+1的值

若n的平方+3n=1,求n(n+1)(n+2)+1的值
若n的平方+3n=1,求n(n+1)(n+2)+1的值

若n的平方+3n=1,求n(n+1)(n+2)+1的值
n(n+1)(n+2)+1
=n(n^2+3n+2)+1 n的平方+3n=1
=3n+1

n(n+1)(n+2)+1
=n(n^2+3n+2)+1
=n(1+2)+1
=3n+1
设y=3n+1
n^2+3n=1
9n^2+27n=9
9n^2+6n+1+21n=9+1
(3n+1)^2+21n+7=10+7
(3n+1)^2+7(3n+1)=17
y^2+7y+49/4=17+49/4
(y+7/2)^2=117/4