Inequality relationship when additing a constant to the denominatorsWhen a b > c d where...

Raul Walker

Raul Walker

Answered

2022-07-10

Inequality relationship when additing a constant to the denominators
When a b > c d where a , b , c , and d are positive real numbers, is a b + 1 > c d + 1 true?

Answer & Explanation

Jenna Farmer

Jenna Farmer

Expert

2022-07-11Added 17 answers

No: 1 2 > 2 5 , but 1 3 = 2 6 .
Pattab

Pattab

Expert

2022-07-12Added 2 answers

a b > c d a d b c b d > 0 a d > b c
Now
a b + 1 c d + 1 = a d + a ( b c + c ) ( b + 1 ) ( d + 1 )
will be < 0 if a d + a ( b c + c ) < 0 a d b c < c a

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