Question

已知a+b=－5，ab=6，求a^2b^2－a^2－b^2+4ab+1

已知a+b=－5，ab=6，求a^2b^2－a^2－b^2+4ab+1的值.

Answer 1

根据a+b=－5，ab=6，得出a^2+b^2+2ab=25，把ab=6带进去，算出a^2+b^2=13
所以a^2b^2－a^2－b^2+4ab+1
=（ab）^2-（a^2+b^2)+4ab+1
=6*6-2*13+4*6+1
=36-26+24+1
=35

Answer 2

a^2b^2－a^2－b^2+4ab+1
=（ab）^2-(a^2+b^2)+4ab+1
=(ab)^2-〔(a+b)^2-2ab〕+4ab+1
=6^2-（5^2-12）+24+1
=36-25-12+24+1
=48

Answer 3

x^2+5+6=0
(x+2)(x+3)=0
a=-2,b=-3或者a-3,a=-3,b=-2
a^2b^2－a^2－b^2+4ab+1
=(a^2-1)(b^2-1)+4ab
=3*8+4*6
=24+24
=48

Answer 4

a^2b^2－a^2－b^2+4ab+1=a^2b^2－（a^2+b^2+2ab）+6ab+1=a^2b^2－(a+b)^2+6ab+1=6^2+（-5）^2+6*6+1=98

Answer 5

a^2+b^2=(a+b)^2-2ab=(-5)^2-2*6=13