Question

已知a=根号3减2,b=根号3加2，分别求下列代数式的值

(1)a^2b-ab^2 （2）a^2+ab+b^2

Answer 1

(1)a^2b-ab^2
解：a^2b-ab^2 =ab﹙a-b﹚
把a=根号3减2,b=根号3加2 代入 ab﹙a-b﹚
=﹙√3-2﹚×﹙√3﹢2﹚×[﹙√3-2﹚﹣﹙√3+2﹚]
=-1×﹙-4﹚
=4

（2）a^2+ab+b^2=（a+b）²-ab
把a=根号3减2,b=根号3加2 代入（a+b）²-ab
=[﹙√3﹣2﹚+﹙√3﹢2﹚]²-﹙√3-2﹚×﹙√3+2﹚
=12+1
=13

Answer 2

a=根号3减2,b=根号3加2
a+b=2√3
ab=-1
a-b=-4

(1)a^2b-ab^2=ab(a-b)=-1(-4)=4

（2）a^2+ab+b^2=(a+b)²-ab=12-(-1)=13

Answer 3

a=√3-2 b=√3+2
(1)a^2b-ab^2
=ab(a-b)
=(√3-2)(√3+2)(√3-2-√3-2)
=[(√3)^2-2^2](-4)
=4
(2)a^2+ab+b^2
=a^2+2ab+b^2-ab
=(a+b)^2-ab
=(2√3)^2-(√3-2)(√3+2)
=12+1
=13