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parmenides51 wrote: For $a,b,c,d \geq 0$ with $a + b = c + d = 2$, prove \[(a^2 + c^2)(a^2 + d^2)(b^2 + c^2)(b^2 + d^2) \leq 25\] https://artofproblemsolving.com/community/c4h1583160p11273596 https://artofproblemsolving.com/community/c4h1583160p11274243

For $ a,b,c,d \geq 0 $and $a + b = c + d = 4. $ Prove that $$\left(a^2+b\right)\left(b^2+c\right)\left(c^2+d\right)\left(d^2+a\right)\le64$$