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- Thu Mar 01, 2018 3:39 pm
- Forum: Secondary Level
- Topic: Problem with complex numbers
- Replies: 0
- Views: 6274
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: $|z_1|=|z_2|=|z_3|.$
- Thu Mar 01, 2018 3:28 pm
- Forum: Secondary Level
- Topic: Inequality with logarithms-please put the complete solution!
- Replies: 0
- Views: 4325
Inequality with logarithms-please put the complete solution!
Let be $a,b,c,d>1$ with $abcd=16$. Prove that:
$log_{ab} (a+b)+log_{bc} (b+c) + log_{cd}(c+d)+log_{da}(d+a) \geq 4.$
$log_{ab} (a+b)+log_{bc} (b+c) + log_{cd}(c+d)+log_{da}(d+a) \geq 4.$