作业帮已知2b=a+c,求证:(a^3+4b^3+c^3)/[b(a^2+c^2)]=3
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![已知2b=a+c,求证:(a^3+4b^3+c^3)/[b(a^2+c^2)]=3](/uploads/image/z/10393472-56-2.jpg?t=%E5%B7%B2%E7%9F%A52b%3Da%2Bc%2C%E6%B1%82%E8%AF%81%3A%28a%5E3%2B4b%5E3%2Bc%5E3%29%2F%5Bb%28a%5E2%2Bc%5E2%29%5D%3D3)
已知2b=a+c,求证:(a^3+4b^3+c^3)/[b(a^2+c^2)]=3
已知2b=a+c,求证:(a^3+4b^3+c^3)/[b(a^2+c^2)]=3
已知2b=a+c,求证:(a^3+4b^3+c^3)/[b(a^2+c^2)]=3
(a^3+4b^3+c^3)/[b(a^2+c^2)]
=[(a+c)(a^2+c^2-ac)+4b^3]/[b((a+c)^2-2ac)]
=[2b((a+c)^2-3ac)+4b^3]/[b(4b^2-2ac)]
=[2(4b^2-3ac)+4b^2]/(4b^2-2ac)
=(12b^2-6ac)/(4b^2-2ac)
=3