已知a+b=3,ab=5/4,求a³b+ab³.

已知a+b=3,ab=5/4,求a³b+ab³.
已知a+b=3,ab=5/4,求a³b+ab³.

已知a+b=3,ab=5/4,求a³b+ab³.
a^3b+ab^3
=ab(a^2+b^2)
=ab[(a+b)^2-2ab]
=(5/4)(9-5/2)
=(5/4)(13/2)
=65/8

a³b+ab³=ab(a²+b²)
=ab(a²+2ab+b²-2ab)
=ab[(a+b)²-2ab]
=(5/4)×[3²-2×(5/4)]
=(5/4)×(9-5/2)
=(5/4)×(13/2)
=65/8