已知(a+b)²=3,(a-b)²=2,分别求a²+b²,ab的值?
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已知(a+b)²=3,(a-b)²=2,分别求a²+b²,ab的值?
已知(a+b)²=3,(a-b)²=2,分别求a²+b²,ab的值?
已知(a+b)²=3,(a-b)²=2,分别求a²+b²,ab的值?
(a+b)²=3,
a²+b²+2ab=3
(a-b)²=2,
a²+b²-2ab=2
两式相加:
2a²+2b²=5
a²+b²=2.5
两式相减:
2ab+2ab=1
4ab=1
ab=1/4
(1)a²+b²=[(a+b)²+(a-b)²]/2=5/2
(2)ab=[(a+b)²-(a-b)²]/4=1/4
(a+b)^2+(a-b)^2=5
a^2+b^2=5/2
ab=(3-5/2)/2=1/4