1. Let prove that
2. Let with . Find the minimum value of
3. Let . Prove that
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In what sense are these "challenge questions"?
In the sense that they are for me
the first and the third inequality can be easily proved by using Cauchy inequality.
By let x+y=r, y+z=t, z+x=s; then the second inequality can be easily proved by using the Mean value inequality!
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