1Ne one trying?????
Come on, this is not so difficult...
Prove that for all real a,b and c satisfying:
a^3+b^3=c^3
the following inequality holds:
a^2+b^2-c^2> 6(c-a)(c-b)
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4 Answers
1try this:
ac=x
bc=y
then
given condition : x3+y3=1
we have to prove: x2+y2-1> 6(1-x)(1-y)
assume x>y
for negative y, x>1 (Hope you come to the same conclusion)
so, 6(1-x)(1-y)<0
but LHS>0
so the inequality is established in this case....
now the case left for us to consider is : 0≤x≤1, 0≤y≤1.
I will leave that for u to try using my hint.