Prove a 4 </msup> + b 4 </msup> &#x2265; a 3 </msup> b

Shea Stuart

Shea Stuart

Answered question

2022-06-29

Prove a 4 + b 4 a 3 b + a b 3 for any ( a , b ) R

Answer & Explanation

Kaylie Mcdonald

Kaylie Mcdonald

Beginner2022-06-30Added 19 answers

Alternatively using AM-GM inequality, we have
a + b 2 a b
or
( a + b ) 2 4 a b a b
so that
( a + b ) 2 a b = a 2 + b 2 + a b 0

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