1.已知a-b=2+根3,b-c =2-根3,则a^2+b^2+c^2-ab-bc-ac的值为( )
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![1.已知a-b=2+根3,b-c =2-根3,则a^2+b^2+c^2-ab-bc-ac的值为( )](/uploads/image/z/657705-57-5.jpg?t=1.%E5%B7%B2%E7%9F%A5a-b%3D2%2B%E6%A0%B93%2Cb-c+%3D2-%E6%A0%B93%2C%E5%88%99a%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%E7%9A%84%E5%80%BC%E4%B8%BA%EF%BC%88+%EF%BC%89)
1.已知a-b=2+根3,b-c =2-根3,则a^2+b^2+c^2-ab-bc-ac的值为( )
1.已知a-b=2+根3,b-c =2-根3,则a^2+b^2+c^2-ab-bc-ac的值为( )
1.已知a-b=2+根3,b-c =2-根3,则a^2+b^2+c^2-ab-bc-ac的值为( )
a-b=2+根3,b-c =2-根3
∴a-c=4
a^2+b^2+c^2-ab-bc-ac
=(2a^2+2b^2+2c^2-2ab-2bc-2ac)/2
=(a²-2ab+b²+b²-2bc+c²+c²-2ac+a²)/2
=[(a-b)²+(b-c)²+(c-a)²]/2
=[(2+√3)²+(2-√3)²+(-4)²]/2
=4+3+8
=15