一题数学题 拜托帮帮忙 有答必赏
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(1)右边 = (1/2) * (a²+b²-2ab + b²+c²-2bc + c²+a²-2ac)
=(1/2)*(2a²+2b²+2c²-2ab-2ac-2bc)
=a²+b²+c²-ab-ac-bc
=左边
(2)∵a²+b²+c²-ab-ac-bc = (1/2)*[(a-b)²+(b-c)²+(c-a)²]
又a = 2009,b = 2010,c = 2011
∴原式=(1/2)*(1 + 1 + 4) = 3
=(1/2)*(2a²+2b²+2c²-2ab-2ac-2bc)
=a²+b²+c²-ab-ac-bc
=左边
(2)∵a²+b²+c²-ab-ac-bc = (1/2)*[(a-b)²+(b-c)²+(c-a)²]
又a = 2009,b = 2010,c = 2011
∴原式=(1/2)*(1 + 1 + 4) = 3
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(1)右边 = (1/2) * (a²+b²-2ab + b²+c²-2bc + c²+a²-2ac)
=(1/2)*(2a²+2b²+2c²-2ab-2ac-2bc)
=a²+b²+c²-ab-ac-bc
=左边
(2)∵a²+b²+c²-ab-ac-bc = (1/2)*[(a-b)²+(b-c)²+(c-a)²]
又a = 2009,b = 2010,c = 2011
∴原式=(1/2)*(1 + 1 + 4) = 3
=(1/2)*(2a²+2b²+2c²-2ab-2ac-2bc)
=a²+b²+c²-ab-ac-bc
=左边
(2)∵a²+b²+c²-ab-ac-bc = (1/2)*[(a-b)²+(b-c)²+(c-a)²]
又a = 2009,b = 2010,c = 2011
∴原式=(1/2)*(1 + 1 + 4) = 3
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