Question

已知a+b=3,ab=-2,求下列各式的值①3a²-2a²b²+3b² ②a²-ab+b²

Answer 1

a+b=3
(a+b)²=9
a²+b²+2ab=9
a²+b²-4=9
a²+b²=13

①
3a²-2a²b²+3b²
=3(a²+b²)-2(ab)²
=3(13)-2(-2)²
=39-8
=31

②
a²-ab+b²
=a²+b²-ab
=13-(-2)
=15

Answer 2

a+b=3,ab=-2
①3a²-2a²b²+3b²
=3（a²+b²)-2a²b²
=3(a+b)²-6ab-2a²b²
=3×3²-6×(-2)-2×(-2)²
=27+12-8
=31

②a²-ab+b²
=(a²+b²)-ab
=(a+b)²-2ab-ab
=(a+b)²-3ab
=3²-3×(-2)
=9+6
=15