若a-b=5,ab=-6,求:(1)a²+b².(2)a²-b².(3)a³+b³.
问题描述：
若a-b=5,ab=-6,求:(1)a²+b².(2)a²-b².(3)a³+b³.
答
a-b=5,ab=-6
(1)a²+b²
=a²-2ab+b²+2ab
=(a-b)²+2ab
=5²+2×(-6)
=13
(2)(a+b)²
=a²+2ab+b²
=13-2×6
=1
∴a+b=±1
a²-b²
=(a+b)(a-b)
=±1×5
=±5
(3)a³+b³.
=(a+b)(a²-ab+b²)
=±1×﹙13+6)
=±19