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已知b+c-a=-2,求2/3a(a-b-c)+b(2/3c-2/3a+2/3b)+1/3c(2b+2c-2a)的值.
题目详情
已知b+c-a=-2,求2/3a(a-b-c)+b(2/3c-2/3a+2/3b)+1/3c(2b
+2c-2a)的值.
+2c-2a)的值.
▼优质解答
答案和解析
代数式2/3a(a-b-c)+b(2/3c-2/3a+2/3b)+1/3c(2b+2c-2a)
=2/3a^2-2/3ab-2/3ac+2/3bc-2/3ab+2/3b^2+2/3bc+2/3c^2-2/3ac
=2/3a^2-4/3ab-4/3ac+4/3bc+2/3b^2+2/3c^2
=2/3(a^2-2ab-2ac+2bc+b^2+c^2)
=2/3(a-b-c)^2
=2/3(b+c-a)^2
=2/3*(-2)^2
=8/3
=2/3a^2-2/3ab-2/3ac+2/3bc-2/3ab+2/3b^2+2/3bc+2/3c^2-2/3ac
=2/3a^2-4/3ab-4/3ac+4/3bc+2/3b^2+2/3c^2
=2/3(a^2-2ab-2ac+2bc+b^2+c^2)
=2/3(a-b-c)^2
=2/3(b+c-a)^2
=2/3*(-2)^2
=8/3
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