Show that sqrt(1+x)<1+x/2 if x>0

Nathanial Levine 2022-09-29 Answered
Show that 1 + x < 1 + x 2 if x > 0
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Answers (2)

Jordan Owen
Answered 2022-09-30 Author has 7 answers
Why not just square both sides?
1 + x < 1 + x + x 2 4
is trivial.
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gsragator9
Answered 2022-10-01 Author has 2 answers
We have that for all x > 0, we have
1 + x < 1 + x + x 2 4 = ( 1 + x 2 ) 2 ,
and hence
1 + x < 1 + x 2 .
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