Question

已知m+n=-4,mn=-12,求n+1/m+1+m+1/n+1的值

Answer 1

(1)
n+1/m+1+m+1/n+1
=(n+m)+(1/m+1/n)+(1+1)
=(m+n)+(m+n)/mn+2
=-4+(-4)/(-12)+2
=-4+1/3+2
=-5/3
(2)
利用完全平方公式m²+n²=(m+n)²-2mn=(-4)²-2×(-12)=40
通分(n+1)/(m+1)+(m+1)/(n+1)
=[(n+1)²+(m+1)²]/(m+1)(n+1)
=[n²+2n+1+m²+2m+1]/(mn+n+m+1)
=[(m²+n²)+2(m+n)+2]/[mn+(m+n)+1]
=[40+2×(-4)+2]/[-4+(-12)+1]
=34/(-15)
=-34/15

Answer 2

解
m^2+n^2=(m+n)^2-2mn=16+24=40
原式
=(n+1)^2/(m+1)(n+1)+(m+1)^2/(n+1)(m+1)
=(n^2+2n+1+m^2+2m+1)/(mn+m+n+1)
=[40+2(m+n)+2]/[(-12)+(-4)+1]
=(40-8+2)/(-16+1)
=34/(-15)
=-34/15

Answer 3