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I have tried to solved the following problem, however, I was stucked. thanks for the help:

x, y z are positive number,

prove (x+y+z)(1/x+1/y+1/z) >=9,

if so, how about (x+y+z+w)(1/x+1/y+1/z+1/w) >= 9.

The following is what I've got:

(x+y+z)(1/x+1/y+1/z) = (x+y+x)[(yz+xz+xy)/xyz]

=[3(xyz) + (x^2*z+x^2*y+y^2*z+x*y^2+y*z^2+x*z^2)]/xyz

= 3 + [(x^2*z+x^2*y+y^2*z+x*y^2+y*z^2+x*z^2)]/xyz

Please help!!!!

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# Inequality math problem

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