若(a+b)²=8,(a-b)²=3,求a²+b²=?ab=?
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若(a+b)²=8,(a-b)²=3,求a²+b²=?ab=?
若(a+b)²=8,(a-b)²=3,求a²+b²=?ab=?
若(a+b)²=8,(a-b)²=3,求a²+b²=?ab=?
依题意
a^2+b^2+2ab=8
a^2+b^2-2ab=3
两式相加
2(a^2+b^2)=11
a^2+b^2=11/2
又
两式相减
4ab=5
ab=5/3
(a+b)²=a²+2ab+b²=8
(a-b)²=a²-2ab+b²=3
两式相加得
a²+b²=5.5
ab=2.5
(a+b)²=8
a²+2ab+b²=64①
(a-b)²=3
a²-2ab+b²=9
①+②
2(a²+b²)=73
a²+b²=73/2
①-②
4ab=55
ab=55/4
a²+b²=[(a+b)²+(a-b)²]/2
=(8+3)/2
=11/2
ab=[(a+b)²-(a-b)²]/4
=(8-3)/4
=5/4
(a+b)²=8 ①
(a-b)²=3 ②
①+②得:2a²+2b²=11
所以,a²+b²=11/2=5.5
①-②得:4ab=5
所以,ab=5/4=1.25
(a+b)^2+(a-b)^2=11
2(a^2+b^2)=11
a^2+b^2=5.5
(a+b)^2-(a-b)^2=5
4ab=5
ab=1.25
若(a+b)²=8,(a-b)²=3,求a²+b²=?ab=?
(a+b)²-(a-b)²=4ab
a+b)²-(a-b)²=8-3
4ab=5
ab=1.25
a²+b...
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若(a+b)²=8,(a-b)²=3,求a²+b²=?ab=?
(a+b)²-(a-b)²=4ab
a+b)²-(a-b)²=8-3
4ab=5
ab=1.25
a²+b²=(a+b)²-2ab
=8-2*1.25
=8-2.5
=5.5
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