已知:(a+b)^2=4,(a-b)^2=6,求a^2+b^2和ab的值

2025-01-01 20:49:56
推荐回答(4个)
回答1:

(a+b)^2=4,(a-b)^2=6
(a+b)^2+(a-b)^2=2a^2+2b^2=10
a^2+b^2=5
(a+b)^2-(a-b)^2=4ab=-2
ab=-1/2

回答2:

(a+b)^2=4 (1)
(a-b)^2=6 (2)
由(1)得
a²+2ab+b²=4 (3)
由(2)得
a²-2ab+b²=6 (4)
(3)+(4)得
a²+b²=5
(3)-(4)得
ab=-1/2

回答3:

(a+b)^2+(a-b)^2
=2a^2+2b^2
=4+6
=10
a^2+b^2=5

(a+b)^2-(a-b)^2
=4ab
=4-6
=-2
ab=-1/2

回答4:

∵(a+b)^2=4,(a-b)^2=6
∴a²+b²=[﹙a+b﹚²+﹙a-b﹚²]/2=5
ab=[﹙a+b﹚²-﹙a-b﹚²]/4=-½