Question

已知(a+b)2=9,(a-b)2=4求a2+b2和ab的值

已知a-1/a=4求a2+1/a2的值

Answer 1

(a+b)²=9
(a-b)²=4
(a+b)²+(a-b)²
=(a²+2ab+b²)+(a²-2ab+b²)
=2(a²+b²)
=13
a²+b²=6.5

(a+b)²-(a-b)²
=(a²+2ab+b²)-(a²-2ab+b²)
=4ab
=5
ab=5/4

补充回答
已知a-1/a=4求a2+1/a2的值
(a-1/a)²=16
a²+1/a²-2=16
a²+1/a²=18

Answer 2

(a+b)^2=9
a^2+2ab+b^2=9

(a-b)^2=4
a^2-2ab+b^2=4
两式相加
2a^2+2b^2=9+4=13
a^2+b^2=6.5
两式相减
4ab=9-4=5
ab=1.25

Answer 3

a2+b2=[(a+b)2+(a-b)2]÷2
=(9+4)÷2
=6.5
ab=[(a+b)2-(a-b)2]÷4
=(9-4)÷4
=1.25