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prove that (1+x)(1+y)(1+z)>(1+xyz)

prove that (1+x)(1+y)(1+z)>(1+xyz)

Grade:9

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
Please find the answer to your question below
if x>0,y>0 and z>0
LHS=(1+x)(1+y)(1+z)
=(1+y+x+xy)(1+z)
=(1+x+y+z+xyz)
=1+xyz+(x+y+z)>1+xyz
from the above it is clear that(1+x)(1+y)(1+z)>(1+xyz)

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