已知(a+b)^2=7,(a-b)^2=4,求ab和a^2+b^2的值.

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已知(a+b)^2=7,(a-b)^2=4,求ab和a^2+b^2的值.
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已知(a+b)^2=7,(a-b)^2=4,求ab和a^2+b^2的值.
已知(a+b)^2=7,(a-b)^2=4,求ab和a^2+b^2的值.

已知(a+b)^2=7,(a-b)^2=4,求ab和a^2+b^2的值.
(a+b)^2=7,
a^2+2ab+b^2=7,
(a-b)^2=4,
a^2-2ab+b^2=4,
相减
4ab=3,ab=3/4,
相加
a^2+b^2=11/2

a^2+b^2=[(a+b)^2+(a-b)^2]/2=11/2
ab=[(a+b)^2-(a-b)^2]/4=3/4

(a+b)^2=7,
(a-b)^2=4
(a+b)^2-(a-b)^2
=4ab=7-4=3
ab=3/4
(a+b)^2=a^2+b^2+2ab
a^2+b^2
=(a+b)^2-2ab
=7-2/3
=19/3