Prove the inequality 1 1 + a + b </mrow>

Brooke Ayala

Brooke Ayala

Answered question

2022-05-19

Prove the inequality
1 1 + a + b + 1 1 + c + b + 1 1 + a + c + a + b + c 3 + 1 3 ( a b + b c + a c )
I used Buffalo way. Can anyone offer an easier way

Answer & Explanation

Ronnie Glenn

Ronnie Glenn

Beginner2022-05-20Added 11 answers

Let f ( a , b , c ) = c y c ( 1 1 + a + b + a 1 a b 3 )
Hence, f is a convex function of a, of b and of c
Thus, max { a , b , c } [ 0 , 1 ] f = max { a , b , c } { 0 , 1 } f = f ( 0 , 0 , 0 ) = 0
Done!

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