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

Nathanial Levine

Nathanial Levine

Answered question

2022-09-29

Show that 1 + x < 1 + x 2 if x > 0

Answer & Explanation

Jordan Owen

Jordan Owen

Beginner2022-09-30Added 7 answers

Why not just square both sides?
1 + x < 1 + x + x 2 4
is trivial.
gsragator9

gsragator9

Beginner2022-10-01Added 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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