MathLabs

Problem 2

Suppose a,b,ca,b,c are the sides of a triangle. Prove that a2(b+c−a)+b2(c+a−b)+c2(a+b−c)≤3abca^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le3abc.
Step 3 of 4: Cancel and simplify
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x2y+x2z+y2x+y2z+z2x+z2y≥6xyzx^2y+x^2z+y^2x+y^2z+z^2x+z^2y\ge6xyz
Detailed analysis

Expanding both sides and cancelling the common terms reduces the desired inequality to the displayed symmetric inequality.