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Old problem in IMOC

Source: 2024 IMOC A8 (Night 6)

August 8, 2024
algebrainequalities

Problem Statement

aa, bb, cc are three distinct real numbers, given λ>0\lambda >0. Proof that 1+λ2a2b2(a−b)2+1+λ2b2c2(b−c)2+1+λ2c2a2(c−a)2≥32λ.\frac{1+ \lambda ^2a^2b^2}{(a-b)^2}+\frac{1+ \lambda ^2b^2c^2}{(b-c)^2}+\frac{1+ \lambda ^2c^2a^2}{(c-a)^2} \geq \frac 32 \lambda.
Old problem, can be found [url=https://artofproblemsolving.com/community/c6h588854p3487434]here. Double post to have a cleaner thread for collection (as the original one contains a messy quote)
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