Question

已知a-b=3 a³-b³=（a-b）(a²+ab+b²) 求a³-b³-9ab/a²-b²-6a的值

如上 谢谢大家解答

Answer 1

已知a-b=3
则a³-b³=（a-b）(a²+ab+b²)=3(a²+ab+b²)
即a³-b³-9ab=3a²+3ab+3b²-9ab
=3a²-6ab+3b²
=3(a²-2ab+b²)
=3(a-b)²
=3*3²
=27
a²-b²-6a
=(a+b)(a-b)-6a
=3(a+b)-6a
=3b-3a
=-3(a-b)
=-3*3
=-9
所以(a³-b³-9ab)/(a²-b²-6a)=27/(-9)=-3
希望能帮到你，祝学习进步O(∩_∩)O

Answer 2

a³-b³-9ab=（a-b）(a²+ab+b²)-9ab=3a²+3ab+3b²-9ab=3(a²-2ab+b²)=3*9=27
a²-b²-6a=(a-b)(a+b)-6a=3a+3b-6a=3b-3a=3*(-3)=-9
a³-b³-9ab/a²-b²-6a=-3

Answer 3

a³-b³-9ab/a²-b²-6a=[(a-b)(a²+ab+b²)-9ab]/[(a-b)(a+b)-6a]=[3(a²+ab+b²)-9ab]]/[3(a+b)-6a]
=(3a²+3ab+3b²-9ab)/(3a+3b-6a)=3(a-b)²/3(b-a)=-3