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anemone
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Let $a,\,b$ and $c$ be positive real numbers such that $a^3+b^3=c^3$. Prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
The given statement is $a^2+b^2-c^2>6(c-a)(c-b) for $a^3+b^3=c^3.
This statement can be proven by using algebraic manipulations and properties to simplify and rearrange the equation until it is in a form that can be easily shown to be true.
The inequality in the statement indicates that the left side of the equation is greater than the right side, which means that the statement must be true for all possible values of a, b, and c.
Proving this statement is important because it is a mathematical truth that can be applied to various real-world situations, and it can also serve as a basis for further mathematical proofs and theories.
Yes, there are specific steps that must be followed to prove this statement, such as identifying and using relevant algebraic properties, simplifying the equation, and providing a logical explanation for each step taken.