Question

已知a²+ab=15，b²+ab=6求a²+b²

Answer 1

a²+ab=15...........(1)
b²+ab=6............(2)
(1)+(2)得
(a+b)²=21...........(3)
(1)-(2)得
a²-b²=9
(a+b)(a-b)=9
(a+b)²(a-b)²=81
(a-b)²=81/(a+b)²=81/21=27/7
(a-b)²=27/7 ...............(4)
(3)+(4)得
(a+b)²+(a-b)²=21+(27/7)
2(a²+b²)=174/7
a²+b²=87/7

Answer 2

a²+ab=15，b²+ab=6
a²+b²+2ab=21

追答

(a+b)²＝a²+b²+2ab=21

a²-b²=9

(a+b)(a-b)＝a²-b²=9

(a+b)²/(a+b)(a-b)＝a+b/a-b=7/3

(a+b)²/(a-b)²=49/9

(a-b)²=(a+b)²×9/49
＝21×9/49
＝27/7

4ab＝(a+b)²-(a-b)²
=21-27/7
=120/7

2ab=60/7

a²+b²=(a+b)²-2ab
=21-60/7
=87/7

a²+ab=15，b²+ab=6
a²+b²+2ab=21
(a+b)²＝a²+b²+2ab=21
a²-b²=9
(a+b)(a-b)＝a²-b²=9
(a+b)²/(a+b)(a-b)＝a+b/a-b=7/3
(a+b)²/(a-b)²=49/9
(a-b)²=(a+b)²×9/49
＝21×9/49
＝27/7
4ab＝(a+b)²-(a-b)²
=21-27/7
=120/7
2ab=60/7
a²+b²=(a+b)²-2ab
=21-60/7
=87/7

Answer 3

两式求和凑完全平方式，求出a+b，然后分别代入两式中得出a，b。最后求值。