another inequality 1 x y + z + 1 y z + x + 1...
Let and such , show that
The theory basis of speculation Use the following classical results
Answer & Explanation
I agree with you. Your inequality is true!
Indeed, the condition gives
Let , and , where and . Hence,
Id est, it remains to prove that for positives , and
Let and , where , and are positive numbers.
Hence, and we need to prove that or