Math Problem Statement

已知：a不等于b，a^2+b=b^2+c=c^2+a

求证：2(a+b+c)=a^2+b^2+c^2+3(bc+ca+ab)

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Simultaneous Equations
Polynomial Equations

Formulas

a^2 + b = b^2 + c = c^2 + a
2(a+b+c) = a^2 + b^2 + c^2 + 3(bc+ca+ab)

Theorems

Symmetry in Equations
Polynomial Identity

Suitable Grade Level

Grades 10-12

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