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by simplythebest
Thu Mar 01, 2018 3:39 pm
Forum: Secondary Level
Topic: Problem with complex numbers
Replies: 0
Views: 273

Problem with complex numbers

Let be $z_1,z_2,z_3 \in \mathbb{C}$ such that $z_1+z_2+z_3=z_1^7+z_2^7+z_3^7=0.$ Prove that: $|z_1|=|z_2|=|z_3|.$
by simplythebest
Thu Mar 01, 2018 3:28 pm
Forum: Secondary Level
Topic: Inequality with logarithms-please put the complete solution!
Replies: 0
Views: 227

Inequality with logarithms-please put the complete solution!

Let be $a,b,c,d>1$ with $abcd=16$. Prove that:
$log_{ab} (a+b)+log_{bc} (b+c) + log_{cd}(c+d)+log_{da}(d+a) \geq 4.$